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AD NUMBER 




THIS PAGE IS UNCLASSIFIED 













UD 

383 

H57 

1952 




T P C H N I C A L 
MEMORANDUM 
ORO-T *160* 




UNCLASSIFIED 

Operational Requirements 



U S ARMY m»UTARY HISTORY INSTITUTE 
CARLISLE BARRACKS, PA 17013-5008 



(or 



an 



OPERATIONS RESEARCH 

OFFICE 

• 

The Johns Hopkins 
University 



INFANTRY 
HAND WEAPON 

By Norman Hitchman 

Statistical Analysis by Scott Forbush and George Blakemore Jr. 



This document is now unclassified, as shown on the 
cover or title page, and all other markings found on any 
pages are obsolete. If any photocopies are made of this 
document, all markings, other than UNCLASSIFIED, 
on each page should be obliterated so that there is no 
misunderstanding of the current classification of any 
information derived from it. 












Operating Under 
Contract with the 

DEPARTMENT OF THE 
ARMY 







FORMATION 



■* 





The contents of ORO publications , including the conclu- 
sions and recommendations, represent the Wews of ORO 
and shou/d not be considered as having official Depart- 
jnanf of the Army approval , either expressed or implied . 




AWC Form 1 Army— CGSC— P2-0236— 9 Aug 51— 25M 

vQ Udv KA 



ciw contains informahon aflFec//ng /he na/iona/ 

defense of the United S fates wi/hin /he mean/ng of /he 
Espionage Laws, Tide 7 8, U. S. C., Sections 793 and 794. 
The /ransmi'ss/on or /he reve/adon of its contents in any 
manner to an unauthorized person is prohibited by law . 




ATION 



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DOWNGRADED AT 3 YEAR INTERVALS: 

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THIS IS A WORKING PAPER 
Presenting the considered results of study 
by the ORO staff members responsible for 
its preparation. The findings and analysis 
are subject to revision as may be required 
by new facts or by modification of basic 
assumptions. Comments and criticism of 
the contents are invited. Remarks should 
be addressed to: , 

The Director 

Operations Research Office 
The Johns Hopkins University 
6410 Connecticut Avenue 
Chevy Chase, Maryland 



' r 



4 ' 



LIBRAS T 

ARMY WAR COLLEGE 




abstract taken by date 



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UNUlftbMriLu, 



OPERATIONAL REQUIREMENTS FOR AN INFANTRY HAND WEAPON 

by 

Norman A. Hitchman 



Statistical Analysis 

by 

Scott E. Forbush 
George J. Blakemore, Jr. 



Of what should a rifle be capable in battle today? Since there is a 
limit/as to how accurately the infantryman fires, can one increase hits 
by giving him a rifle with new operational characteristics? ORO’s 
Project BALANCE studied this by talcing data on how often, and by 
how much, riflemen missed targets (as well as the distribution of 
hits) at different ranges, by talcing data on the ranges of engagement 
in battle, and by talcing data on the physiological wound effects of 
shots with differing ballistic characteristics. The recommendation 
is made that Ordnance proceed to determine the technological 
feasibility of a weapon with operating characteristics analyzed iii 
this memorandum. This follows from conclusions whjch are listed 
only sketchily below: 

Hit effectiveness using the M*1 is satisfactory only 

* up to 100 yards and declines very rapidly to low 
order at 300 yards, the general limit for battlefield 
rifle engagements. 

A pattern-dispersion principle in the hand weapon 

• would tend to compensate for human aiming errors 
and increase hits at ranges up to 300 yards. 

Missiles, smaller caliber than now standard, ‘could 
^ be used without loss in wounding effects and with 
logistical advantage, and a great increase in hit 
lethality could be effected by using toxic missiles. 



Abstract page from: O RO" T- 1 60 

LASSIF 

(xM + 105 pp, 51 Figs., 11 Tables) 
Received: 19 dune 1952 

Proiect BALANCE 



OPERATIONS RESEARCH OFFICE — The Johns Hopkins University 



IMfBM CONlUd WITH 1 H I D ■ M I I W E H T OF THE ARMY 





Log No., 



81938 



Copy No 




This Document contains information affecting the Nafiona/ Defense 
of the United States within the meaning of the Espionage Laws, 
Tit/e IS, U.S.C., Sections 793 and 794 . The transmission or the 
reve/ation of its contents in any manner to an unauthorized person 
is prohibited by law . 



THIS ABSTRACT IS OF A WORKING PAPER 

Presenting the considered results of study by the 
ORO staff members responsible for its preparation. 
The findings and analysis are subject to revision as 
may be required by new facts or by modification 
of basic assumptions. Comments and criticism of 
the contents are invited. Remarks should be ad* 
dressed to: 

The Director 

Operations Research Office 
The Johns Hopkins University 
6410 Connecticut Avenue 
Chevy Chase, Maryland 








Technical Memorandum ORO-T-160 

^OPERATIONAL REQUIREMENTS FOR 
AN INFANTRY HAND WEAPON 

by 

Norman A^[itdiman 

Statistical Analysis 

by 

Scott E. Forbush 
George J. Blake mo re, Jr* 



LIBRARY 

ARMY WAR COLLEGE 
CARLISLE BARRACKS, PA. 

Received: 19 June 1952 

Project BALANCE 




OPERATIONS RESEARCH OFFICE, 

jV V|irj ■ - ^ 

The Johns Hopkins University. 

Chevy Chase, Maryland 




SECUI 



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Unclassified 



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Published 
November 1952 
by 

OPERATIONS RESEARCH OFFICE 
6410 Connecticut Avenue 




Unclassified 



ACKNOWLEDGMENT 



The author gratefully acknowledges the 
valuable assistance given by Col. E. M. 
Parker, Project Chairman, in the prep- 
aration of this study; especially were his 
paraphrases welcomed, for they crystal- 
lized areas of thought where otherwise 
the author would have faltered. 







CONTENTS 



Page 



ABSTRACT 

ACKNOWLEDGMENTS 

SUMMARY 

Purpose — Assumptions — Discussion — Conclusions 
Recommendations. 

OPERATIONAL REQUIREMENTS FOR AN INFANTRY 
HAND WEAPON 
Introduction 

COMBAT CASUALTY STUDIES 

Former Studies — Lethality of the Rifle — Rifle 
Bullet Hits as a Function of Range in Combat — 
Man-Rifle Operations Studies. 

TERRAIN VISIBILITY STUDIES 

Range Requirements and Tactical Employment 
of Hand Weapons — Map Analysis. 

THE RIFLEMAN AND HIS WEAPON 

Marksmanship: Tests and Analyses — The Pattern 
Salvo Weapon — Full -Automatic Fire — Wound Bal- 
listics: Missile Caliber, Mass, and Velocity. 

LETHALITY 

Weapons in General — The Rifle — Comparison of 
an Ideal Dispersion Automatic with M-l Single- 
Shot Fire — Can Lethality Be Increased? 

THE DISPERSION WEAPON 

Basis of Issue (T/O&E) — Training — Design 
Feasibility. 



5 

7 

10 

15 

25 

31 




ix 




CONTENTS (Continued) 



Page 



A THEORY FOR DETERMINING RELATIVE EFFEC- 



TIVENESS OF DIRECT FIRE WEAPONS 
Method Used. 


35 


CONCLUSIONS 


40 


REC O MME NDATIONS 


40 


BIBLIOGRAPHY 


42 


APPENDIX 


43 



Analysis and Application of Results of Rifle-Range 
Tests. 



FIGURES 

1. Comparison of Battlefield Visibility in Korea 

anrj Ranges of Employment of the M-l Rifle. 10 

2. Frequency Distribution for Ranges of Contin- 
uous Visibility for Terrain Classes A, B, and C. 12 

3. Method Used in Measuring Range of Visibility 

on Maps. 14 



4. Marksmanship Using the M-l Rifle. IV 

5. Comparison of Lethality per Aimed Shot or 

Burst for the M-l and the Salvo Automatic. 28 

6. Rifle Marksmanship, Battlefield Visibility, 

and Hit Probability in Combat. 37 

7. Theoretical Distribution of Hits as Function of 

Range for M-l Rifle and a Salvo-Type Hand Wea- 
pon for Terrain Classes A, C. 38 

8. Relative Effectiveness of M-l Rifle and Salvo 

Automatic for Terrain Classes A, C. 39 



UH iOl* 



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CONTENTS (Continued) 



TABLES 

1. Computed Distribution of Hits as Function 
of Range R. 



2. Relative Effects of M-l Single -Round Fire 
and Salvo Fire as Function of Range for 
Terrain Classes A and C. 



Page 



36 



38 




xi 



SUMMARY 



PURPOSE 

The study reported upon in this memorandum was undertaken 
for the purpose of determining the desirable operational char- 
acteristics of a general purpose infantry hand weapon. 



ASSUMPTIONS 

It has been assumed that it is desirable to increase in both 
number and rate the hits which may be inflicted on the enemy by 
aimed small arms in the hands of the infantry. 

It has been further assumed that it is desirable also to 
increase the mortality of wounds caused by these hits. 



DISCUSSION 

In this examination of the basic infantry weapon, the rifle, 
two commonly accepted considerations or premises were care- 
fully scrutinized, and their bearing upon infantry operations 
evaluated: 1) the time taken to hit enemy man targets is vital 
in that hits should be inflicted as early and at as great a range 
as possible; and 2) these hits should inflict significant injury — 
should be at least immediately incapacitating (in some circum- 
stances, lethal). The findings are generally affirmative with 
respect to both propositions. 

Study of combat records of operations, as well as field 
investigations of the man-rifle combination, shows that much is 
to be gained by increasing the hit capability of aimed rifle fire 
at the common battle ranges, and that increasing the severity of 
the hits is also to be sought. How men actually use the rifle in 
combat, the ranges of engagement most frequently recurring 
in battle, how terrain limits inter visibility of opposing firing 




SECURI^^f^jMBfMRlFOetAATION 




lines, and what is required ballistically to create physiologically 
desirable wound effects on the enemy, are factors which have 
been analyzed for the purpose of determining the operational 
requirements of a general purpose hand weapon. 

Study of the various factors involved has yielded a number 
of independent but related and consistent determinations. Syn- 
thesis has permitted comprehensive evaluation of the combat 
actions bearing in concert upon effective employment of the 
hand weapon. 

Battlefield visibility data show why combat rifle fire is 
actually so limited in range by normal terrain obstructions to 
the line of sight as rarely to exceed 300 yd. Studies of the 
manner in which gunshot wounds are incurred in battle suggest 
that lesser -included ranges are in reality the important ones. 
Measurements of marksmanship show that performance is of 
a very low order beyond a range of 300 yd. Wound ballistic 
data offer convincing evidence that small caliber, high velocity 
missiles may be used profitably at such ranges, without loss 
in wounding effects and with significant logistical gains. 

The mutually confirmatory nature of the several findings 
goes far to explain present rifle operations, and to suggest the 
desirable characteristics for a general purpose infantry hand 
weapon. The conclusions which follow have emerged. 

CONCLUSIONS 

1. The ranges at which the rifle is used most frequently in 
battle and the ranges within which the greater fraction of man 
targets can be seen on the battlefield do not exceed 300 yd. 

2. Within these important battle ranges, the marksmanship 
of even expert riflemen is satisfactory in meeting actual battle 
requirements only up to 100 yd; beyond 100 yd, marksmanship 
declines sharply, reaching a low order at 300 yd. 

3. To improve hit effectiveness at the ranges not covered 
satisfactorily in this sense by men using the M-l (100 to 
300 yd), the adoption of a pattern-dispersion principle in the 
hand weapon could partly compensate for human aiming errors 
and thereby significantly increase the hits at ranges up to 300 yd. 

4. Current models of fully automatic hand weapons afford 
neither these desirable characteristics nor adequate alterna- 
tives. Such weapons are valueless from the standpoint of 
increasing the number of targets hit when aiming on separated 
man- size targets. 



2 




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5. Certain of tl 




ccuracy observed 



in the manufacture of current rifles and ammunition can be 
relaxed without significant losses in over -all hit effectiveness. 

6. To meet the actual operational requirements of a general 
purpose infantry hand weapon, many possibilities are open for 



panying increases in hit probability) at the ranges of interest. 

Of the possible salvo or volley automatic designs,* the small 
caliber, lightweight weapon with controlled dispersion char- 
acteristics appears to be a promising approach. (Low recoil 
of a small caliber weapon facilitates dispersion control.) 

7. To create militarily acceptable wound damage at common 
battle ranges, missiles of smaller caliber than the present stand- 
ard .30 cal can be used without loss in wounding effects and with 
substantial logistical and over -all military gains. 

8. A very great increase in hit lethality can be effected by 
the addition of toxic agents to bullet missiles. 

RECOMMENDATIONS 

1. It is recommended that the Ordnance Corps proceed to 
determine the design or technological feasibility of developing 
a hand weapon which has the characteristics cited in this 
analysis, namely: 

a. Maximum hit effectiveness against man targets 
within 300 yd range. (This does not mean that the weapon will 
be ineffective beyond this range. ) 

b. Small caliber (less than .30). 

c. Wounding capability up to 300 yd at least equivalent 
to the present rifle. 

d. Dispersion of rounds from salvos or burst controlled 
so as to form a pattern such that aiming errors up to 300 yd 

^Current military usage of the two words salvo and volley is confused. By “salvo” the 
Navy and Air Force generally mean, respectively, the simultaneous discharge of several 
pieces, or the simultaneous release of a number of bombs; the Army usually employs the 
word to indicate the successive firing of several guns within a single command unit. 
“Volley” is commonly taken by all services to mean the simultaneous firing of a number 
of rifles or guns, with the exception that the artilleryman often applies the word to the 
independent (unsynchronized) firing of a certain specified number of rounds by each of 
several associated pieces. What is discussed here and in the following pages is either 
a simultaneous, or a high cyclic rate, burst , with the number of rounds per burst auto- 
matically set rather than dependent upon trigger release. In the former design, con- 
trolled nutation of the rifle muzzle would provide the desired shot dispersion or pattern; 
in the latter, the scatter would be obtained and controlled by multiple barrels, a mother- 
daughters type of projectile, or projection of missiles in the manner of a shotgun. 



designs which will give desirable dispersion patterns (and accom- 



ORO-T-160 




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SECURITY, 




SECURITY-, 



^FORMATION 



Unclassified 

will be partly compensated, and hit effectiveness thereby 
increased for these ranges. 

2. As one possible alternative to the current "volume of 
fire" (fully automatic) approach to the problem of increasing 
the effective firepower of infantry riflemen, it is recommended — subject 
to tentative confirmation of design feasibility— that a rifle incor- 
porating at least in principle the military characteristics here 
proposed be manufactured for further and conclusive test. 












jject 



OPERATIONAL REQUIREMENTS FOR AN INFANTRY 

HAND WEAPON 

(INTRODUCTION 

The subject of this study is of a basic nature for it applies 
to the basic weapon of the basic branch— the rifle carried by the 
infantry. Because the hand arm offers certain capabilities not 
duplicated by any other means, and because it is basic to the 
whole weapons system, the effectiveness of that weapon in battle 
is a subject of first importance in any general consideration of 
the whole fire system. It follows that any study directed toward 
a comprehensive examination of the aggregate of weapons for the 
purpose of designing and proportioning a “balanced" system 
(the mission of Project BALANCE) may logically take a beginning 
with this basic ground weapon. 

Such an approach is, moreover, timely at the moment in the 
sense that the NATO is confronted now by an urgent requirement 
for standardization of a general purpose hand weapon for the 
infantry. Thus, any information which may be cogently pertinent 
to such weapons will have a bearing on an immediate problem of 
some moment. 

The study here presented has been carried out not only in 
full recognition of the importance of improving the effectiveness 
of infantry, but also in growing awareness that the task — even 
though so basic in nature— is an exceedingly complex one. The 
effort has thus far been only preliminary. Limited time, and 
inadequate knowledge of basic unit operations in combat, have 
restricted the degree to which the whole problem might be 
examined. Consequently, no complete solution is offered by this 
memorandum; rather, some analytical findings are presented, 
which suggest the principles governing certain measures which 
could be undertaken to improve infantry effectiveness with 
respect to aimed rifle fire. 

This memorandum bears directly upon the importance and 
the use by infantry of aimed small arms fire in the front line 



ORO-T-160 




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IMATION 



Unclassil 




tactical fire fight, but does not consider expressly the impor- 
tance, the techniques or the effects of unaimed u covering fire 1 ’ 
delivered by small arms. The reason for directing the study 
effort toward aimed fire is that the common arm of the infantry, 
the rifle, is designed primarily for the aimed fire role; that is, 
the weapon is designed expressly to afford a capability of directing 
missiles at observed man-targets with high inherent precision, 
in both offensive and defensive action. Delivery by such a weapon 
of covering fire to neutralize or pin down the enemy and permit 
friendly maneuver is tactically useful, but nonetheless amounts 
to a secondary role for which design has provided only inciden- 
tally, The important question at hand, therefore, is not so much 
connected with the varying actual use of the present firearm as 
with the need of the infantry to engage the close enemy effec- 
tively by the use of aimed rifle fire, and with the feasibility of 
incorporating in the rifle of general issue the capability of 
answering this real requirement. 

Recent ORO investigations in Korea have shed some light 
on this subject by indicating quantitatively the comparative 
importance of aimed and unaimed fire as related to offensive 
and defensive operations. Generally, aimed fire plays a more 
important part in defense than unaimed or volume fire, whereas 
in the offensive, the reverse is true Almost irrespective of 
the part played by the supporting weapons before or during the 
final phase of close combat, the decision in each small tactical 
battle rests ultimately in large measure with the infantryman 
and his ability to use his hand weapon effectively. If hand-to-hand 
fighting develops at all, decision thus rests almost entirely with 
the infantry in this last time -phase of the tactical situation. To 
attach importance to this aspect of battle is therefore logical, 
and the attempt to maximize the capability of infantry in this 
role cannot be misdirected effort. 

The study has yielded suggestions for increasing infantry 
effectiveness by improving the effects of aimed rifle fire. It 
appears almost certain that future large-scale ground operations 
will involve a numerically superior enemy and necessitate, at 
first, a defensive strategy on our part. Morever, frequent 
attempts to overrun infantry positions, with attendant close 
combat, are to be anticipated. Thus, to increase each infantry - 



highly desirable. 

In the light of such considerations as these, it appears correct 
to assume that: 1) it is desirable to increase in both number and 



man's capability with respect to defensive rifle fire becomes 



6 




1 



ORO-T-160 






ified 

rate the hits which may be inflicted on the enemy by aimed small 
arms in the hands of the infantry; 2) it is also desirable to increase 
the mortality from wounds caused by these hits. 

The research effort has included examination of casualties 
of past wars, studies of terrain as it limits battlefield visibility, 
determination of the marksmanship of men, wound ballistics 
requirements, actual use of the rifle in combat, and other 
considerations bearing on military operational requirements 
for the general purpose hand weapon. The determinations 
arrived at from the study of present rifle fire and its effects 
are presented in the following sections. 



I 






COMBAT CASUALTY STUDIES 



Former Studies 

Earlier work done by ORO on the defense of the individual in 
combat, 1 and a preliminary study of the offensive capabilities 
of the rifle, 2 yielded definite indications that rifle fire and its 
effects were deficient in some important military respects, and 
that further study of the problem would be necessary fully to 
establish the facts. In these former studies it was found that, 
in combat, hits from bullets are incurred by the body at random: 
regional distribution of bullet hits was the same as for fragment 
missiles which, unlike the bullet, are not "aimed. " Further, 
it was found that exposure was the chief factor responsible for 
the distribution of hits from bullets and that aimed or directed 
fire does not influence the manner in which hits are sustained. 31 
Stated briefly, the comparison of hits from bullets with those 
from fragments showed that the rifle bullet is not actually better 
directed towards vulnerable parts of th e body. 

The discovery of these facts, along with evidence of prodi- 
gious rifle ammunition expenditure per hit, strongly suggested 
the need to extend the study of the rifle problem. The facts 
known at this point also prompted one to regard with some 
dubiety the employment of the present, highly accurate, pre- 
cision-made rifle as a general purpose infantry weapon. It 
should be noted, .however, that complete verification would not 
suggest elimination of a precision long-range rifle to be used 

‘Footnote numbers refer to publications listed in Bibliography. 

Multiple hits on the same target are much less to be desired than a large number of 
targets hit. 




ORO-T-160 



7 



by some men highly skilled and selected for specialist opera- 
tions, e. g. , snipers. 

Lethality of the Rifle 

As for the combat importance of hits from rifle bullets as 
compared to other weapons in the ground system, historical 
studies show that bullets have accounted for 10 to 20 percent 
of all hits from all ground weapons in most battles, campaigns, and 
wars of this century. 4 Although these figures qualitatively provide 
a measure of the relative capability of hitting the opposed infantry- 
man, they do not disclose capabilities with respect to severity of 
injury. Of these two factors (simple wounding and extent of injury) 
which characterize weapons effects, not much is known about either 
in the sense of cost versus effect because ammunition expenditures 
and corresponding casualty -producing effects are not usually known 
with precision. On the other hand, aside from the closely related 
machine gun, the rifle is the most lethal of all conventional ground 
arms: its lethal index (ratio of kills to hits) exceeds 30 percent, 
putting it above other weapons in capability of inflicting severe 
injury.* The lethal index of the machine gun, of course, exceeds 
that of the rifle because multiple hits increase over -all lethality. 
For bullet lethality, the 30 percent figure given for the rifle would 
be the closest approximation to single round lethality for all ranges 
in battle . 

Rifle Bullet Hits as a Function of Range in Combat 

Knowledge of the ranges at which hits have been incurred in 
past wars is sharply limited. Since this parameter is almost indis- 
pensable to the military specialist or operations analyst in deter- 
mining weapons effects, it is astonishing that greater efforts in the 
past have not been directed toward gathering information of this 
kind in combat operations. 



*In this analysis, the figure 30 percent refers only to enemy weapons of World War II 
type but since enemy rifles did not differ greatly from our own, the lethal index value 
should approximate that of the M-l rifle. Strictly, lethal refers here to the bullet, rather 
than the rifle, which is the launcher. What is meant is that a larger fraction of the total 
bullet hits results in death than from hits from any other weapon. The explanation does 
not lie in the manner in which rifle bullets are directed, since data show that bullet 
hits occur on the body at random just as do hits from fragmenting projectiles and there- 
fore their relatively high lethality is not connected with any bias in their distribution 
over the body. The reason appears to be connected with the higher (and more nearly 
constant) energy, on the average, than other missiles since they are discharged at short 
ranges. Fragments, however, vary in energy from a maximum to zero, with the mean 
value being relatively low because of the preponderance of small fragments per missile 
burst and because of the rapid deceleration of particle velocities with range. 



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Unclassified 



Only two studies exist which have reference to bullet hits as 
a function of range in battle, and they are based on indirect and 
possibly inaccurate measurements. Oughterson® analyzed expe- 
rience on Bougainville in World War II and found that, of those 
cases studied, almost all rifle bullet hits were received at ranges 
less than 75 yd.* The Surgeon General recently examined the 
wounded in Korea, and from a sample of 109 rifle bullet hits 
suffered among members of the Turkish Brigade, the mean range 
for these hits was found to be just over 100 yd.* It was noted, 
however, that most of the hits occurred at ranges within 300 yd 
and in a later section of this report these data along with data on 
battlefield visibility will be given more extensive treatment. 

Man-Rifle Operations Studies 

The British AORG during World War II, and ORO in FECOM, 
have both attempted to study part of the man-rifle complex by 
interviewing experienced riflemen on their use of the weapon in 
offensive and defensive combat actions. The British examined 
officers and NCOs who had experience in the ETO 7 and ORO 
examined men with experience in Korea. 8 The agreement of the 
two independent studies is striking. For attack and defense in 
European actions, it was found that about 80 percent of effective 
rifle and LMG fire takes place at less than 200 yd and 90 percent 
at less than 300 yd, according to the estimates made by the men 
interviewed. About 90 percent of the LMG fire was at less than 
300 yd. 

Of 602 men questioned about use of the M-l rifle in Korea, 

87 percent said that at least 95 percent** of all their firing was 
done at targets within 300 yd range (day time offensive fighting)." 
For day time defensive fighting, 80 percent of the men said that 
rifles were used at 300 yd or less. Figure 1 shows the frequency 
in which rifles are used as a function of range, based on responses 
of interrogated infantrymen. The approximate correspondence of 
the curves in the Figure indicates that the use of the rifle is to at 
least some extent dependent upon battlefield terrain features as 
they affect visibility.*** Although it is freely acknowledged that 
the use of data derived from judgments of the men about the use 
of their basic arm may be subject to question, the validity of the 

* 

This figure is perhaps atypically low because it refers to jungle fighting in which 
^visibility was abnormally restricted. 

The men were asked to give the outside limit of 95 percent of their firing in order to 

eliminate those rare shots which might be fired at long ranges without expectation of 
^ hitting the target. 

See section on battlefield visibility. 




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opinion survey has been substantiated by a more recent Korean 
study conducted in combat areas . 5 Also, as mentioned earlier, 
the analysis made by AORG tends to support the conclusion that 




Fig. 1 — Comparison of battlefield visibility in Korea and ranges of 
employment of the M-l Rifle. 



the infantry basic weapon is actually used, on the average, at 
shorter ranges than commonly believed. 

TERRAIN VISIBILITY STUDIES 

Range Requirements and Tactical Employment of Hand Weapons 
Despite the important role of infantry support weapons (artil- 
lery, tactical aviation, armor, and others), the entire ground 
weapon system hinges in many important ways upon those weapons 
which depend for their effective employment upon ground obser- 
vation of the target . These are the direct-fire and observed-fire 
weapons ; they are elemental, basic, and indispensable to the 
infantry-artillery-armor team. 

Unclassifie 



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For infantry, the basic direct fire weapon is the rifle— it is 
the common denominator upon which the entire fire system is 
designed, both physically and tactically. Yet all direct-fire 
weapons suffer a major weakness in that essential observation 
for their effective employment may be obscured by weather 
conditions, prevented by darkness or— more importantly and 
quite unavoidably— interrupted by terrain features. This inter- 
ruption of the line of sight is one of the principal military effects 
of terrain, for the ranges at which points on the ground are inter - 
visible are related to the employment and general effectiveness 
of these direct-fire weapons. Accordingly, terrain limitations to 
continuous visibility on the battlefield should dictate to a consid- 
erable degree the actual design and employment of direct-fire or 
observed-fire weapons. A study of this subject which was under- 
taken by Project BALANCE and which is covered in detail in a 
separate report, 10 has yielded formulary expressions for the 
relationship between the opening range of engagement for riflemen 
and the range at which man-targets can be seen. Particularly with 
respect to the rifle, the study is basic in its concept and possibly, 
for the first time, data have been obtained which constitute a 
reasonable quantitative basis for determining the actual range 
requirements and tactical employment of a general-purpose 
hand arm. 

Because of the importance of these findings to the infantry 
weapons problem, they should be studied carefully in conjunction 
with the work presented here on operational requirements for an 
infantry hand weapon. 



Map Analysis 

Topographical map studies of a number of large scale (1:25,000) 
maps of various countries in the world have shown that it is pos- 
sible to predict, with reasonable accuracy, the probability of being 
able to see continuously for a given distance from a random point 
within the area. 10 

For the infantry study, the procedure used in the map analyses 
was to measure the continuous ranges of visibility between infantry- 
men, with the position of one man (the defender) being at ground 
level (foxhole or prone) and the approaching enemy being an erect 
human target five feet high. This factor was chosen to set realistic 
limits on the range of iiit$r visibility betwqen^opposing forces. The 

unclassified 



ORO-T-160 



11 



validity of the map readings was verified by actual terrain meas- 
urements* and the findings are in general agreement with limited 
combat data from the Korean experience and ETO experience dur- 
ing World War II.** 

From the map study, it was found that all the types of terrain 
so far considered fall into one of three categories which are illus- 




0 500 1000 1500 

R (YD) 



Fig* 2 — Frequency distribution for ranges of continuous visibility for Terrain Classes 
A, B, and C. (Probability of seeing man-targets at ranges greater than R yards from a 
random point within the area covered by the map analysis.) 



* Tests were conducted on the battlefield area of Gettysburg in which a small party of 
ORO analysts checked map predictions by actually walking over the terrain in accord- 
ance with the map bearings and measuring the distance of intervisibility. In every 
instance, distances of continuous visibility were found to be less than the distances 
predicted by map measurement because of terrain features and obstacles not shown on 
maps. Map readings were considered, therefore, to represent maxima. 

The mean ranges of visibility from map analyses of Korea and Normandy show remark- 
able agreement with limited combat knowledge of ranges of engagement between 
riflemen and between tAnks. In Korea, the frequency of ranges for bullet hits agreed 
with the frequency of ranges for visibility. For World War II tank battles, both Peterson 
of Ballistics Research Laboratory and ORO (Ref. 10) have shown that ranges of engage- 
ment for tanks correspond with ranges of visibility in the battle areas as determined 
from map analysis. These two samples of combat data tend to validate the use of the 
map data for predicting range requirements. 




ORO-T-160 



* 



linin'* SECRET- 



1 




sified 



trated by the three curves in Fig. 2. The frequency distribution 
for Type A terrain is typical for a country like the Saint-Lo area 
in Normandy, where visibility is sharply limited by the masses of 
hedgerows, small cultivated fields, orchards, and the nature of 
the terrain itself. Type A also describes rugged, mountainous 
terrain like Korea. The distribution curve for Type C describes 
relatively open country where the topography is gently rolling and 
large, open, cultivated areas exist. Type B is intermediate between 
the two extremes cited and describes an average type of cultivated 
countryside. 

The importance of these data to the infantry study is related 
to the range requirements for infantry weapons and, as shown in 
Fig. 2, 95 percent of all observations include ranges which are much 
less than the range capabilities of many of the infantry direct fire 
weapons. The implication that such weapons may be over -designed 
is appreciated when it is considered that the rifle alone has a 
maximum range capability of 3,500 yd. 

The following description of the procedure used in the map study 
is presented so that the practical application of the data may be 
recognized. 

Figure 3 shows diagrammatic ally a corner section of a 1:25,000 
map. The method of measurement was adopted from a suggestion 
by Peterson of Ballistics Research Laboratory who used map grid 
lines as guides for sampling any given terrain. 

The analysis of each map is begun at Point A (northwest corner). 
Proceeding along the east-west grid line, the distance is measured 
from the edge of the map to the point where an erect (five feet) 
infantryman would just be obscured from the sight of a defending 
prone infantryman at Point A. In this case, the crest of a hill 
(contour) is the factor which obstructs visibility. After recording 
the distance A to B, the next point of obscuration is measured by 
proceeding along the grid line from Point B to Point C where a 
railroad embankment interrupts the line of vision. Distance BC 
is then recorded and so on along the grid line to the far edge of 
the map. It will be noted that a house or building limits visibility 
at Point D and woods limit vision at Point E. 

After all horizontal grid lines are measured in this way, the 
same method is used on all vertical grid lines. Then all the obscu- 
rations from one map are used to plot a frequency distribution. 
Examples of such frequency distribution have been given already 



in Fig. 2. 




ORO-T-160 



13 



SfCftET 



1 ^ 
r j' 






Although the frequency tlistri^utioh curyes yield predictions as 
to the probability of seeing man targets at Range R, from any ran- 
dom point on the terrain, it may be argued that infantrymen are 
not randomly located along the front but actually take up positions 
which have been selected for point of advantage (for example, high 
ground in the defence). So far as this is true for small units such 
as squads and platoons especially in defensive positions, such biases 
as a result of the placement of men are not systematic, and when 
division or corps fronts are considered, the density of men and 
their positions across a broad front can be considered to be more 



Edge of Map 




Starting at the northwest corner of the map one looks from the point A / where the first hori- 
zontal grid line begins, along that grid line to the point B where, because he has gone over 
the crest of a hill, the standing infantryman (the target) ceases to be visible. The distance 
AB is measured and recorded. Next, starting from B, one finds that the target is continu- 
ously visible until the railroad embankment at C causes obstruction to view; the distance 
BC is then measured and recorded. Similarly, starting from the top of the embankment, it is 
clear that there is no obstacle until one reaches the house at D; CD is measured and 
recorded. Next the distance DE is recorded; then, starting from the eastern edge of the 
wood, the distance to the next obstruction is measured; and so on across the map to the 
right margin. After all horizontal grid lines have been followed in this way, one starts 
again at the northwest corner and reads from F down the first vertical grid line and all the 
other grid lines. All the readings obtained in this way are used to plot a frequency distri- 
bution. Figures 2 through 7 are examples of such frequency distributions. 




14 



ORO-T-160 



or less uniform. Thus, in relation to terrain, their position is 
more nearly random. Also, no systematic selection of ground is 
permitted either side during a battle, since position, which is 
fluid and constantly changing, is dependent upon the whole battle 
situation and not just upon ground features. Therefore, the random 
selection on a map of a battlefront in any given terrain should pre- 
dict the actual ground condition of the battlefield. In general, it is 
felt that men move in battle in a more or less random manner, so 
the data obtained in the visibility study are reasonably valid for 
predicting the probability of seeing targets over any area, particu- 
larly since the method used measured the type of movement used 
by troops in battle, that is, from cover to cover. 

Employing this method, map studies of Canada, France, Germany, 
Korea, North Africa, and the US, to a total of some 18,000 readings, 
showed that 70 percent of the ranges at which an erect human target 
can be seen by a defending prone rifleman are less than 300 yd (and 
that 90 percent are less than 700 yd). 

Since range requirements exert a considerable if not dominating 
influence upon such characteristics as weight, caliber, and missile 
velocity, the data from the map analyses have a very important 
bearing upon the design of an infantry hand weapon. Comparing the 
range analysis data with the maximum range of the present M-l 
rifle (3,500 yd), and its design for incapacitating clothed personnel 
up to 1,200 yd, it may be concluded that the effective rang es of the 
greater part of infantry hand weapons cou ld be reduced materially 
to an order suggested by the terrain analysis. (A reduction of the 
range of the rifle for maximum effectiveness up to 300 yd does not 
mean that the weapon would not be effective at ranges beyond this. ) 



THE RIFLEMAN AND HIS WEAPON 

Marksmanship: Tests and Analyses 

The preceding sections have described, to some extent, certain 
major factors dictating the actual operational requirements for the 
general-purpose hand arm of infantry. Since marksmanship obviously 
plays a major role in the over -all effectiveness of hand weapons em- 
ployment in the military situation, the measure of the varying capa- 
bilities of combatants to use their weapons with tactical effectiveness 
becomes, along with target visibility, a significant parameter in the 
whole infantry study. 

To provide meaningful data on this subject, field tests were con- 
ducted at Fort Belvoir, Virginia, where 16 expert riflemen (highest 



ORO-T-160 









15 



grade) and 16 marksmen (lowest qualified grade) were used in a 



series of experiments designed to simulate some of the conditions 
of combat. The 32 men were divided into groups for two sets of 
tests. Firing the M-l rifle from the prone position, using battle 
sights, they shot at a man- silhouette target operated on a tran- 
sition-type range, at distances of 100-300 yd. Mounted behind the 
silhouette was a 6 foot high by 12 foot wide screen; on this could be 
measured the dispersion of rounds. The target butts were draped 
with OD cloth so that short rounds, not striking the target, could 
also be recorded. (These experiments and the results are described 
in detail in the Appendix. ) 

Further data were procured from a range test on automatic 
rifles at Fort Benning, Georgia.* 

In the tests at Belvoir, a variety of conditions was imposed on 
the participants chiefly by changing the time of target exposure 
and imposing forms of psychological duress. It was found that 
best results were obtained when single rounds were fired on an 
individual basis at-sfatic man-size targets. Marksmanship 
declined when group firing (4-man groups) was performed at the 
same targets. With slight psychological load, in the form of 
limited target exposure time and random order of presentation 
at varying ranges, a further decline in effectiveness was noted. 

Hit probability as a function of range for both grades of riflemen 
is shown in Fig. A4 (Appendix). 

Significant results from these analyses are: (a) hit probability 
is high for both grades of riflemen at ranges up to 100 yd; (b) at 
ranges beyond 100 yd, a sharp decline in hit probability occurs 
and this decline in effectiveness is most marked at the common 
battle ranges, between 100 and 300 yd; (c) at 500 yd, both experts 
and marksmen perform unsatisfactorily, a performance quite 
inconsistent with the design capability of the weapon and with 
military specifications.** 

These findings provide part of the explanation for most fre- 
quent battle use of rifles at ranges less than 300 yd and for the 

The author acknowledges the assistance of Lt Col D, E, Munson of ORO in arranging 
for these tests and in helping with test designs which were in keeping with the 
practical aspects of conditions of combat. 

**For the issue M-l rifle and standard M-2 ammunition, the mean radial dispersion is about 
ten inches at a range of 500 yd. An indication of the discrepancy existing between the 
inherent accuracy of the weapon and ammunition, on the one hand, and that of the man- 
rifle combination, on the other, may be found by comparing miss probabilities at the 
range of greatest interest, namely 300 yd. In a machine or bench rest, the probability 
that the rifle- ammunition combination will miss the type E silhouette target (which 
approximates the head and torso region of an erect human target — projected area about 
4.6 sq ft) at 300 yd is about PM = .040; whereas, for marksmen firing individually, the 
probability of a miss is Pm - 0.76. 




16 



ORO-T-160 



I HIPUMMtm 




incurrence of the majority of rifle bullet wounds in combat within 
this range. Since deflection errors in aiming are independent of 
range (Appendix), the sharp decrease in hits beyond 100 yd is not 
to be attributed to men becoming less accurate at the longer ranges 
the hit probabilities shown by the curves are a function of target 
size and range. 




A Experts individually firing new weapon 
B Experts firing individually 
C Marksmen firing individually 
D Marksmen firing simultaneously 

Fig. 4 — Marksmanship using the M-l Rifle 

(Probability of hitting target as function of range) 



The difference between expert riflemen and marksmen, 
although significant at some ranges in these tests, may or may 
not be meaningful in actual combat where man targets will be in 
movement and psychological duress will be high. In fact, in the 
rapid fire tests using targets randomly presented (see Appendix, 
Test 3), the marksmanship of experts declined significantly when 
compared to simultaneous firing in Tests 1 and 2. The same 
comparison for marksmen showed that the rapid fire test did not 
significantly affect their performance, indicating, perhaps. 



ORO-T-160 



17 



that under the rigorous conditions of combat, only slight differ- 
ences exist in marksmanship among the several qualifications as 
determined on the range. 

In a fire fight, it is reasonably certain that marksmanship 
will be less effective than shown by the curves in the tests which, 
for this reason, are presumed to be optimistic as relating to the 
actual situation. 

In connection with the dispersion inherent in the weapon and 
in the ammunition used, it is interesting to note that, at all com- 
mon ranges, weapon errors are without significance in the man- 
weapons system. As already pointed out, considerable discrepancy 
exists between the accuracy of the weapon and that of the riflemen. 
In the Appendix, it is shown that the -dispersion of the weapon could 
be more than doubled without materially affecting the probability 
of hitting the target. As shown in Fig. A43, weapons -design 
standards which seek perfection by making the rifle more accurate 
(approach zero dispersion) would not be reflected in improved 
marksmanship or musketry. Such high standards of precision and 
accuracy on the part of present designers are not supported by 
this analysis as genuine military requirements. Results of 
the analysis on marksmanship were also used to predict the value 
of using a weapon which would tend to compensate for man-aiming 
errors by firing a pattern salvo, or volley.* In Fig. 4, one of 
the examples of hit effectiveness for such a weapon is presented 
(from the Appendix). 

The Pattern Salvo Weapon 

As shown by field test, errors in aiming have been found to be 
the greatest single factor contributing to the lack of effectiveness 
of the man-rifle system. In particular, the men who are graded 
by Army standards as expert riflemen do not perform satisfactorily 
at common battle ranges, a fact which casts grave doubt on any 

The results of the tests on marksmanship already have astonished many persons 
because it was not expected that men would exhibit such low performance at the 
common ranges. The factors which possibly explain the disparity between the higher 
marksmanship scores from Army training methods, when firing on known distance 
ranges, and the lower scores from the ORO tests are apparently connected with the 
conditions of the tests which neither simulated Army methods of scoring or approached 
the true conditions of combat. Perhaps by adopting training methods along the lines of 
the tests conducted, the performance of men might show some general improvement. In 
any case, the test results are believed to be more indicative of the actual capabilities 
of riflemen in a military situation than the qualification score made when firing for 
record on the range. The ORO test data already have been used in other analyses 
relating to the weapons system and have proven of great value. Because they may prove 
useful to other workers in military analysis, the Appendix has been written to include 
most of the raw data in the form of tables and figures, resulting in “bulk” for which 
there is no other warrant. 



ORO -T- 160 



g * " 11 11 'SEC RE T 




attempt at the development of skills through training which would 
begin to approach the accuracy of the weapon itself. Although care- 
ful selection and intensive training of personnel in the use of the 
rifle may accomplish much in improving marksmanship in peace 
time, the problems of rapid Army expansion and accelerated train- 
ing in time of national mobilization preclude the opportunity to 
develop highly skilled riflemen in large numbers by selection or 
through prolonged training. This point is often overlooked by those 
who argue for better training as the only solution for the rifle pro- 
blem. Actually, to reach truly proficient standards in marksman- 
ship, the time required in training would greatly exceed the prac- 
tical limits imposed on Army training schedules by the needs of 
mobilization.* 

In the search for alternatives to an extensive (and impracticable) 
training program, consideration was given to the possibility of 
compensating for man-aiming errors through a weapon-design 
principle. The results of the marksmanship study indicate that a 
cyclic or salvo-type automatic fire arm offers promise of increasing 
hit effectiveness if the missiles in a burst or salvo were projected 
so as to be dispersed randomly or uniformly around the point of 
aim. Obviously, a uniform type of dispersion would be more 
desirable than random dispersion if hit effectiveness were to be 
maximized. In considering such a weapon, two points required 
determination: (a) a practical limit on the number of rounds per 
burst or volley; and (b) the pattern design of the rounds to be 
delivered. 

In the Appendix, the consideration of four- and five -round 
salvos was not arbitrary. Wound ballistics data show that small 
caliber missiles of high velocity could be used in the new weapon 
(see section on Wound Ballistics), which suggested the possibility 
of obtaining logistic equivalence (that is, equivalence in weight of 
weapon and ammunition carried) between a four -round salvo and 
present single-shot rifle fire**; also, not less than four rounds 
would be required to form a symmetrical pattern (diamond- shaped) 

One expert rifleman at Fort Be nning, Georgia , estimated that it required nine years of 
continuous training on fire arms to develop marksmanship to the proficient level which 
he now enjoys. Sgt. Justice’s performance in demonstrating the use of infantry hand 
weapons is most dramatic. His skill in marksmanship actually approaches the accuracy 
of the weapon; he has attained a level of performance roughly commensurate with the 
design precision of the weapon. However, it is estimated that less than 10 percent of 
the men in the normal recruit stream could possibly reach this level of small arms 
proficiency, even if time allowed for training were long. 

* * 

Calculations actually reveal that, for a high velocity, .21 cal missile of 60 grains, the 
ratio of cartridge weights for M-l standard ball ammunition and the small caliber rounds 
would be about 1.6 : 1. 



ORO-T-160 19 





around the point of aim which would tend to maximize hit prob- 



ability on the human-target shape.* 

As shown in the Appendix, a cyclic or salvo-type hand weapon 
would materially increase the effectiveness of aimed fire among 
the infantry. Although not all possibilities in pattern dispersions 
and numbers of rounds were analyzed, it appears that the best 
design (for the greatest practical gains) is one using the four- 
round salvo with 20 in. spacing among rounds at 300 yd range. 
The development of a salvo weapon having these characteristics 
represents an ideal toward which effort might be directed; it is 
not suggested that this is the only solution. 

By considering the need to maintain minimal logistic require- 
ments (number of rounds) and minimum weight, a weapon which 
conformed to the principle of this design would tend to optimize 
the military effects of a fire arm, per se. To add to these gains 
materially, an impractical number of rounds per salvo or 
burst, or an entirely different weapon would be required** 

From the analysis of the dispersion of shots fired at various 
ranges, it was possible to calculate the relative effectiveness of 
a hypothetical new type, salvo automatic weapon, which was 
assumed to differ from the M-l rifle only in the manner in which 
the missiles were projected. Examples of the effectiveness of 
four- and five-round salvos with 20 in. spacing among rounds at 
varying ranges are given in Figs. A41 and A42. It will be noted 
that a four-round salvo of 20 in. spacing at 300 yd would more 
than double hit effectiveness at this distance. Coincidentally, 
this increase, through a design change alone, would raise the 
performance of common marksmen using the salvo weapon to the 
level of expert riflemen using the M-l. 

From this analysis of marksmanship and its relation to a 
given weapon, it is concluded that: (a) The marked decrease in 

*The analysis (Appendix) suggests that the human target is represented reasonably well 
by a circular shaped target. Since the average projected area of the body in combat is 
less than 2 sq ft* and a man is about 20 in. wide, the average human target is thus more 
nearly represented by a rectangle approximately 12 in. X 20 in. if the profile of the 
head on the shoulders were not considered. Considering the head, however, the average 
human target in combat does approximate a circle. 

A hand weapon could be designed like a Very pistol and project small fragmentation 
shells which could be directed at the enemy in much the same way as grenades. By 
using the new principle of controlled fragmentation shells and employing some unique 
time fuze, it might be possible to reach a level of true maximum effects for fire arms. 
The problem would be connected with the fuze and not the launcher if missile bursts 
were to be controlled over the heads of the enemy. Such a weapon would require 
considerable technical development, involving, probably, a longer range program than 
a pattern-dispersion-type fire arm. Any contemplated plan for proceeding with the 
development of fragmentation hand arms should cause the dispersion weapon to be an 
intermediate step in the developmental chain. 



20 




ORO-T-160 



1 



INFORMATION 

C 

* it* o H 

ifey 



hit probability occurring between 100 and 300 yd suggests that 
significant improvement in effectiveness at these ranges cannot 
be achieved by increasing the ballistic accuracy of the weapon: 
aiming errors are too great to be compensated by any improve- 
ment in the accuracy of the rifle alone, (b) A cyclic or salvo 
automatic weapon could compensate largely for these aiming 
errors if the missiles were projected with a dispersion pattern 
designed to maximize the probability of a hit on the human target 
at ranges which most frequently recur in combat (up to 300 yd). 



Full -Automatic Fire 

The last conclusion prompted an examination of the opera- 
tional performance of current models of fully automatic rifles 
to determine whether these desirable characteristics obtained. 
Two questions were salient: (a) As the fully automatic rifle is 
ordinarily aimed and fired, what is the nature of the shot dis- 
persion from short bursts? (b) Does automatic fire in short 
bursts increase the probability of a hit on a man-size target, 
especially at ranges of 100 to 300 yd? 

To answer these questions, tests were arranged at Fort 
Benning, Georgia, in which both expert riflemen and marksmen 
used current models of full automatic rifles. Type E silhouette 
targets were mounted in front of six by six-ft target screens. 
The first firing serial was at 100 yd using controlled bursts of 
five rounds each. Never did more than one round hit the target 
or screen from any of the short bursts, and consequently no 
information could be obtained at 100 yd on the nature of the 
dispersion pattern. To obtain more than one strike on the six 
by six-ft screen, the range had to be closed to 50 yd. At this 
short range it was noted that the man- silhouette target in front 
of the screen was not' hit more than once from any burst. Since 
single round firing with the M-l rifle at 50 yd yields a proba- 
bility of hit of near unity, the effectiveness of automatic fire 
at such short ranges was of no interest. 

The results of these trials (although preliminary) strongly 
suggested that the emphasis and impetus currently being placed 
by the US and other NATO countries on the development of fully 
automatic hand weapons should be questioned on the basis of 
actual military requirements for the automatic feature. ORO 
plans to make further tests* of infantry weapons and some of 
these tests will include further work on shot dispersions of 



It is planned to :stablif 



ORO-T-160 



tactical research laboratory at Fort Benning, Georgia. 




21 




5E' 



infantry hand arms. However, any work bearing on the estab- 
lishment of military requirements for weapons, especially 
automatic hand arms, should provide operational data upon 
which decisions can be made. In this connection, it might be 
pointed out that the tests on automatic rifles conducted at Fort 
Benning, Georgia, do not constitute the type of weapons eval- 
uation from which such requirements can be established. In 
the reports of these tests, 11 the weakness of automatics from 
an operational effectiveness standpoint was not revealed, and 
it is unfortunate that such large-scale trials should not have 
been designed scientifically to produce data upon which such 
facts might be determined. Any comparison of automatic and 
semiautomatic weapons should be designed to determine military 
effectiveness by relating hit effectiveness with fire power, to 
include rate of expenditure. 

From the preliminary, yet informative, tests conducted by 
ORO on automatic hand arms it may be stated that: 

1. Regardless of the skill of the rifleman, only the first 
round in a short, fully automatic burst can actually be directed 
at a point target. 

2. At normal battle ranges, all shots after the first fall off 
a man- size target in an approximately linear pattern, the pro- 
gressively greater departures* depending in magnitude upon 
the characteristics of the weapon and the manner in which it is 
held. 

3. At all common battle ranges, with present hand-held 
automatics, the strike dispersion is so great that moving the 
center of impact for the burst to the center of the target would 
not increase the number of hits. 

4. Even at much reduced ranges, where more than one hit 
from a short burst is scored on a man-size target, the use of 
a burst can be justified only in a limited sense, since at 
these ranges single rounds (semiautomatic) have a probability 
of near unity of striking the target. It follows that reducing the 
range does not increase the probability of hitting with automatic 
fire,** but only of obtaining multiple hits, Moreover, when at 
ranges of 50 yd or less, multiple hits become probable, the 

*The rifleman, by a more or less difficult compensating effort, may exert a type of 
control. Such control is in itself erratic and is not noticeable before 5-10 rounds 
have been fired, according to the cyclic rate of the weapon. 

*This result is inconsistent with current rifle design, which provides a high rate of fire 
in an effort to increase the number of targets hit, as compared with, say, the model 1903 
rifle. Thus, automatic fire is not to be justified oil the basis of an increased proba- 
bility of obtaining &hit on separated man-size targets. 




22 



ORCUT-160 



ry 



f 



ire 

.903 



160 




lethality of the burst increases much more slowly than does the 
number of hits (see section on lethality). 

5. The full automatic feature of current infantry weapons is 
valueless from the standpoint of increasing the number of targets 
hit when aiming at separated man- size targets.* 

Wound Ballistics: Missile Caliber, Mass, and Velocity 

Wound ballisticians have recently determined that the "wound- 
ing power" or damage capability of a missile is more nearly 
proportional to the cube of the velocity than the square. 12 A 
reasonable (and acceptable) measure for wound severity is the 
maximum volume of the temporary cavity produced in the tissue 
by a penetrating missile. It has been found, for example, that 
the effect of increasing the velocity of a small caliber missile 
more than compensates for the reduced mass. Recent work 11 
has shown that, if extreme ranges are not important, a smaller 
caliber bullet than the present .30 cal US military standard 
might well be used. Moreover, evidence shows that at common 
ranges, .22 cal bullets can produce wounds of measurably 
greater severity than .30 cal bullets striking with the same 
velocity, providing these velocities at target are greater than 
a certain critical value. 

Although more extensive work will be required in inves- 
tigating the effects of nose shape, weight, and other factors as 
they affect flight characteristics and wounding ability, it has 
been established that smaller bullets can be used to produce 
battlefield physiological effects at least equivalent to those of 
the present standard .30 cal. Substantial logistics savings would 
also accrue from the introduction of substantially lighter and 
less expensive cartridges, although actual savings cannot be 
expressed quantitatively until further research indicates the 
most practical weight and shape of bullet to employ. The areas 
of incomplete research should be investigated at the Biophysics 
laboratory, the Army Medical Center, Edgewood, Maryland, 
where facilities and skilled personnel offer the opportunity to 
advance knowledge in this field in a reasonable length of time 
and in an important way. 

* 

During the course of this study, the author considered the various possible uses of 
present automatics in combat where the automatic feature (and the wide dispersion of 
rounds) would be militarily useful. Discussion with experienced infantry combat 
commanders and other military specialists led to the conclusion that although the 
feature was useful in tight, close-in positions, usually another weapon (e.g., a grenade) 
could be used to greater advantage than could a burst from an automatic. Also, it was 
indicated that, for the average rifleman, such occasions were rare and did not consti- 
tute a basis for justifying the feature. 



ORO-T-160 








Quite apart from the idealized concept of a salvo weapon, 
sufficient evidence is at hand to be quite certain that a light, 
high-velocity, small caliber rifle could be designed for military 
use and could fulfill effectively the role of a general purpose, 
lightweight hand arm. 

In a recent study 14 conducted by D.L. Hall of the Terminal 
Ballistics Laboratory, Aberdeen Proving Ground, a theoretical 
comparison of the effects and military usefulness of various 
calibers of rifles shows that, when the combined weight of wea- 
pon and ammunition is held constant to 15 lb, the over-all 
expected number of kills for the .21 cal rifle is approximately 
2.5 times that of the present standard .30 cal rifle. When 
compared to M-l ammunition, a .21 cal missile of high velocity 
(about 3500 feet per second muzzle velocity) creates equal or 
greater damage than the standard .30 cal missiles at ranges 
up to 800 yd. This evidence, combined with the work of Proj- 
ect BALANCE (ORO) on ranges of visibility, marksmanship, 
and actual operational needs, lends considerable support to 
the major conclusion that lighter hand weapons of smaller 
caliber may well be provided without losing military effec- 
tiveness, while offering both impressive logistical gains and 
improved operations. 

In addition to these gains, the advantages of low -recoil 
effects offered by the smaller caliber weapons would be reflected 
in improved skill in the use of the weapon by allowing a higher 
rate of single -round aimed fire. Such weapons would also be 
much less fatiguing to handle. Since recoil of a small caliber 
weapon would be less than that of present weapons, the disper- 
sion of rounds in a short, fully automatic, burst could be 
considerably less than the dispersion of current models. This 
important characteristic, yet to be determined by actual trial 
of small caliber automatics, might possibly be the most prac- 
tical solution to the problem of developing an automatic fire 
arm which will project missiles in a burst such that the dis- 
persion of rounds, at ranges up to 300 yd, would approach the 
ideal dispersion for maximum effects as indicated in the 
Appendix. 

The studies and experimental development work* currently 
being undertaken by the Ordnance Corps at Aberdeen Proving 

Discussion with G. A. Gufstafson of the Small Arms Section of BRL indicated that it is 
feasible to design small caliber, high velocity, automatic rifles, which would exhibit 
short-burst dispersion patterns at ranges up to 300 yd, tending to approach 
dimensionally the ideal patterns outlined in the Appendix. 



24 





ORO-T-160 



SB 



LATION 



PWTORMATION 



1 ! 

U 



\ 



I * \ 



&ddlifo 




Ground should be encouraged to proceed toward a rifle develop- 
ment which will fulfill these important military characteristics. 
Although such a light weapon would not compensate for human 
aiming errors when fired semiautomatically, it is quite possible 
that automatic fire in short bursts at common battle ranges 
would produce dispersion patterns commensurate with the 
requirements of the idealized salvo weapon. In particular, the 
low recoil of a small caliber rifle offers the chance to employ 
a muzzle compensator with significant effects, lending added 
promise to a satisfactory development. If the development of 
this light, high velocity weapon could proceed to include the 
ideal salvo principle, obviously a truly effective hand arm 
could be provided. 



LETHALITY 



Weapons in General 

The history of the development of weapons and tactics shows 
an interesting process of self -adjustment. It has been found, 
from an examination of many campaigns from Marathon to 
Korea, that battles are no more bloody now, despite vastly 
"improved" weapons, than they were in the days of the short 
sword: the casualties incurred per number of men 

engaged per unit of time remains about constant.* In fact, 
it may well be that the sword is much more lethal than con- 
ventional weapons because it can be directed with more 
control at the vulnerable areas.lt remains to be seen whether the 
tactical use of atomic and new CBR weapons will alter this 
trend. 

The explanation for this apparent constancy in the intensity 
of battle effects seems to be related to the compensating 
changes in tactics which each new weapon introduces. Most 
advances in weapons either increase the distance over which 
a blow can be delivered (improved launcher) or increase the 
lethal radius or radius of effect (improved missile), or both. 

The ratio of the lethal area to the concentration (or density) 
of enemy targets appears to have remained constant. Since 
logistics costs have markedly increased since the early wars, 
war itself has become vastly more costly in terms of the 
effect-cost ratio, yet little if any more effective in terms of 
personnel casualties per unit time or per unit effort. 



From an unpublished ORO study. 



| W' ' 

f A f Q l t * ir * o. a 






ION 



ORO-T-160 



25 



Although these are measures of gross intensity for war 
(total casualties only), it is interesting to note that severity 
of weapons as measured by their lethality has not changed, 
at least in the past century. If the lethal indices of weapons 
(also a constant) could be raised, efficiency and effect might 
well be improved materially, and no compensating tactical 
adjustment would be practicable. It is believed that the 
means for doing this are at hand, and, with special reference 
to one weapon (the infantry hand arm), an estimate is made 
in a following section of expected results if bullet lethality 
were increased, as seems technologically feasible. 

The Rifle 

The lethal index of a weapon corresponds roughly with 
tactical effectiveness since it refers to those wounds which 
are speedily lethal, the condition of which cannot be reversed 
by medical intervention. Since, by this definition, "lethal 1 ' 
effects result in death very quickly (or death is assured), 
the lethal index is a measure of tactical effect. Therefore, 
in the forward areas of the combat zone, where bitter hand- 
to-hand fighting occurs, there is no sound basis for arguing 
against the merit of disposing of the enemy in the shortest 
possible time by inflicting maximum physical trauma. For 
the infantry hand arm, the infliction of severe wouifds, that 
are immediately incapacitating, is important. 

As stated earlier, the lethal index of the rifle exceeds 
30 percent when hits at all ranges are considered, and, 
with the exception of the machine gun, it is the most lethal 
weapon of all conventional missile projecting ground arms. 

Comparison of Lethality of an 

Ideal Dispersion Automatic with M- 1 Single -Shot Fire 

From Table A9 and Fig. A40 in the Appendix, it is pos- 
sible to estimate the lethality of an ideal dispersion weapon 
at the various battle ranges and compare these effects with 
those of the rifle. Because no exact information exists 
concerning the vital area complex of the body or the effects 
on lethality of multiple hits, it was necessary to assume that 
all bullets from a salvo, or burst, are independently lethal 
and that multiple hits are incurred at random relative to the 
vulnerable areas. Obviously, this assumption ignores the 
fact that physiological effects of multiple wounds are cumu- 
lative (shock, exsanguination, and the like), and that hits 



26 



ORO -T -160 



e 



1 



4 




^ if*' o 

Ifjj i j • J 




from the ideal dispersion weapon follow a pattern design and 
do not, therefore, strike at random. Since cumulative effects 
of multiple wounds add to lethality, and since any lack of 
randomness in the hits may or may not favor the probability 
of striking mortally vulnerable areas, the estimates given may 
be strengthened perhaps by the compensating effects of these 
two indeterminate factors. For each weapon, is assumed 
that the lethal probability of a bullet hit is O.3.* 

From Table A9 (Appendix]^ the lethality for the dispersion 
weapon (five -round salvo pattern) can be estimated for each 
category of single and multiple hits for each range. An 
example of the method used is given for a range 200 yd: 
Probability of kill per bullet hit, PI = 0.3; 

Probability of not killing per hit, Ps = 0.7. 



Thus, for each category of possible hits from a five-round salvo: 



Hits 


Ps 


PI 


1 


0.700 


0.300 


2 


0.490 


0.510 


3 


0.343 


0.657 


4 


0.240 


0.760 


5 


0.168 


0.832 



For range 200 yd (Table A9), the probabilities of obtaining 
exactly 1, 2, 3, 4, and 5 hits with the five -shot patterns are: 



Hits 


1 


2 


3 


4 


5 


Ph** 


0.388 


0.122 


0.284 


0.0580 


0.000 



therefore, 

PhxPl = 0.116 0.0622 0.187 0.0441 0.000 



At range 200 yd, the probability of killing an enemy per 
burst is the sum of the lethal probabilities = 0.409. 

For single rounds from the M-l rifle at 200 yd, the kill 
probability is 0.135 (Ph = 0.45 and PL = 0.3, Fig. A40). In 



The lethal index of the rifle bullet exceeds 30 percent. It is assumed that the smaller 
caliber bullet for the new weapon would be equally lethal since it will have a wounding 
capability equal to or greater than the M-l at the ranges involved. 

The variations noted in the probabilities for obtaining more than one hit are due to the 
shape of the human target as it affects a strike of two or more hits from the dispersion 
pattern. 



f fnnfn 


_ « 




(J 1 [LI H 


1 i | 


* K + t 



-160 



ORO-T-160 



27 









TION 



this way, the lethality of the two weapons may be compared 
as shown in Fig. 5. 

The curves giving the lowest lethal limit* and the prob- 
able upper limit for the dispersion weapon show that a 
considerable relative increase in lethality over the rifle may 
be expected through the use of the dispersion weapon for 
ranges beyond 100 yd. The theoretical upper limit would 



x 



H- 

LU 

_J 

LL 

O 

>- 



CD 

< 

CD 

O 

a: 

Q. 





RANGE (YD) 



Fig. 5 Comparison of lethality per aimed shot or burst for the M-l Rifle and 

the Salvo Automatic. 



exceed the M-l rifle by about a factor of three, if the basic 
assumptions used in the estimates can be accepted as rea- 
sonably valid. Obviously, at ranges less than 100 yd, the 
dispersion of the rounds in the salvo pattern becomes greatly 
diminished as range is decreased. Consequently, the lethal 
effects will not differ greatly from the single -round rifle 
especially when zero range is approached. This variation 
in pattern size with range points up the difficulty of attempt- 
ing to assess comparative lethal effects at the shorter ranges 
and also reveals the weakness of the estimates at the greater 
distances. 





IMATION * 




Quite apart from any consideration of or comment upon, 
the protocols and conventions according to which the rules of 
land warfare have been codified, it is proper to estimate in 
a purely physical way the results of the use of toxic missiles 
in such weapons. 

Consequently, Fig. 5, the two weapons have been com- 
pared for a use of toxic missiles.* It is interesting to note 
that, by the addition of toxic missiles to the M-l rifle, the 
lethal effects thus produced are about equivalent to the 
theoretical upper limit on physical effects given for the dis- 
persion weapon. On the other hand, the employment of toxic 
missiles in the dispersion weapon offers, in toto, still greater 
gains; such effects would constitute an order of lethality not 
achieved by any missile projecting ground weapon yet devised. 

Can Lethality Be Increased? 

The lethal indices of present weapons cannot be improved 
materially (if at all) by increasing the effective "hitting power" 
alone, since the mortally vulnerable regions of the body set 
a limit to the gain. However, by combining chemical toxi- 
cants with physical missiles, it is possible to make the entire 
body vulnerable by utilizing the circulatory system as, in 
effect, a "missile track" which produces certain lethal effects. 
Rather than 30 percent fatalities derived from bullet hits, this 
procedure would cause the body to become mortally vulnerable 
to virtually all of the hits received. Quite apart from the 
relative increase in lethality brought about by the design of a 
dispersion weapon as shown in the preceding section, the 
following analysis on toxic missiles has been included to show 
the nature of the relative gains to be expected in the dispersion 
weapon if toxicants were introduced in future warfare. The 
gains to be described are purely speculative and would provide 
additional gains only to the physical lethality of the dispersion 
weapon. Although not a necessary adjunct, should toxicants 
be employed, the smaller missiles suggested for the new wea- 
pon would be more efficient vehicles of the agent than the 
larger .30 cal bullets. 

Developmental work in the field of toxic missiles is rea- 
sonably complete and shows that up to 90 percent of hits from 
agent-loaded bullets at common ranges may be expected to 

*As indicated later, a lethal probability P = 0.9 was assigned to each toxic loaded 
round. The curves were established by taking the product of the probability of a hit 
and the probability of lethality for toxic missiles. (See Table A9 and Fig. A40.) 



f f 

l I ^ 



-160 



ORO-T-160 



29 







nplq nr* 

incapacitate in a matter of minutes and bring about death 
regardless of the region of the body struck. 15 The agent 
used is stable (in storage, it is as stable as any other part 
of the round); it can be manufactured in large supply at low 
cost; its toxicity is about as high as any substance known. 

The physiological effects produced by the agent are similar 
to the G- agents: death is rapid and the course of the effects 
is violent. The progress of the physiological symptoms is 
demoralizing to witness; thus real psychological effects not 
normally characteristic of weapons design are added.* 

Since it has been found that small missiles (such as .22 
cal) are more efficient vehicles for such toxic agents than are 
the larger calibers/ 5 the application of toxic missiles to a 
small caliber hand weapon as herein proposed is particularly 
adaptable. To the increase in hit effectiveness brought about 
by the use of the dispersion weapon, an impressive gain in 
the lethality of these hits might be added. Thus would be 
achieved a genuine innovation in a weapons system which has 
exhibited through history a constancy in lethal effects.** 

Data from the last two World Wars show that for ground troops 
the ratio of killed to wounded (all ground weapons) was, for both 
periods, about 1:4.1. About 20 percent, then, are killed in action. 1 
With the single addition of toxic bullets for small arms to the 
whole weapons system, the ratio of KIA to WIA in these past two 
wars would have been raised from 1:4.1 to about 1:2.1, or, on 
the average, the lethal index of all weapons would have increased 
12 percent, from 20 percent to 32 percent.*** 

Although these figures are crude estimates of the gross 
or over -all gain which might be expected by the employment 
of toxic missiles, it is probable that the gain would be a 




Apart from flaming weapons, ordnance development has not taken advantage of possible 
designs to produce fear in the enemy as well as physical damage. Toxic missiles do 
offer the possibility of combining the elements of physical and psychological trauma for 
maximum effects. [See also ORO-B-3, Appendix H, (SECRET)] 

Against toxic missiles, certain defense measures could be adopted. A suitable antidote 
could be carried by each man in the form of an ampule and injection could be performed 
through the clothing using the same methods as planned for defense of G-agent 
poisoning. Also, if small caliber missiles were used and the bullets were designed to 
encourage rapid disintegration in the wound track, light (plastic) armor might be used. 

In both of these areas of defense, the Soviet may be weaker than the US in the initial 
phases of toxic missile employment but it is certain that, like all other technical 
advantages in warfare, a process of neutralization will occur whereby neither side has a 
material advantage because of the equalizing effects of the defense measures which 
both sides eventually adopt. Furthermore, speedy retaliation in kind should not be 
difficult for either side. 

Enemy reactions must be anticipated. 



30 



™>^ - I 



ORO-T-160 



* 



SEO 



NATION 




strategic one rather than tactical* In an ORO analysis of 
battle casualties as to their period of non-effectiveness, 16 
data indicate that ideal toxic missiles would do little further 
to reduce enemy strength during any battle situation but may 
exert considerable influence over an extended campaign. 

Finally, it must be remembered that only by improving the 
hit capability of the weapon, as herein proposed in the dis- 
persion weapon, would one expect maximum gains in the 
tactical situation if toxic missiles were introduced. 

THE DISPERSION WEAPON 
Basis of Issue (T/OkE) 

It is to be emphatically stated that the new type hand arm, 
as proposed in this study, should not entirely replace the longer - 
range rifle in the unit organization. In most tactical situations 
there is a definite requirement for sniper (highly specialized) 
fire. It is also important to maintain a degree of versatility 
responsive to the dynamic tactical situation. Consequently, it 
is believed that the precision-aimed, long-range rifle must be 
retained for that limited but existing employment which its 
design characteristics actually fit. Limited knowledge of sniper 
fire indicates that at squad level it is not employed frequently 
in the fire fight but has an important role in the defense or in the 
less fluid conditions (maneuvering for build-up, and so forth) 
preceding a hot action* As far as can be determined by ques- 
tioning combatants, the ranges of sniper fire are mostly within 
the tactical damage range of the small caliber, high velocity 
missiles (i, e. , up to 800 yd). This suggests the possibility of 
using weapons of the same caliber as the general purpose hand 
arm, but designed for precision, long-range use. However, 
the whole question of sniper fire in battle is yet to be analyzed 
from an operations point of view; until this is done little can be 
said concerning weapons requirements for specialists in this role* 



About 20 percent of the total hits of these past wars have been bullet hits. Of those hil 
roughly 30 percent are KIA. (On limited knowledge of enemy Japanese rifles of WW XT.) 
Thus, toxic bullets would result in 90 percent KIA among those hit and increase the 
lethality of the bullet by a factor of 3*. Thus the total killed by bullets would increase 
from, 20 X 0.3 — 6 percent to 20 X 0.9 = 18 percent. The total killed (all weapons) 
would then increase from 20 percent to 32 percent of those hit, (Note: The figure, 6 
percent, for fatal bullet hits may be low for small arms fire; Tribby’s analysis of 1,000 
KIA in the ETO attributed about 11 percent of those killed to small arms fire.) 



ORO-T-160 




31 



SECUR 




* IP* 3 

\ & 







\ ? ^ ^ ? t,7m 

The question of< a general purpose hand arm is not one of 



supplanting a long-range precision arm, but rather of replacing 
a certain number with a different weapon, each type having its 
own proper and effective tactical application. 

It is believed that a practical and useful beginning can be 
made in deciding upon the optimum ratio of short-range hand 
arms to long-range precision rifles by noting the figures for 
ranges of engagement which have been presented earlier. On 
the average, it has been found that 70 percent of the ranges over 
which a man-size target is visible to a defending rifleman lie 
within 300 yd. Since the short-range weapon will be designed 
according to specifications for maximum effect up to 300 yd, 
it may be suggested that 7 in every 10 infantry hand weapons 
should have the characteristics desirable for short-range use. 
Although this target- visibility criterion, employed to set an 
upper limit to the range of engagement, ignores certain vari- 
ables within the small infantry unit which bear on control and 
communications as well as many of the problems of musketry 
and maneuver, it may be received as a tentative and preliminary 
basis for issue. 

Another approach to the determination of an optimum ratio 
for hand weapons is to consider the aptitudes of enlisted men 
normally received from the manpower pool. From experience 
at Fort Benning;* the development of no more than two expert 
riflemen per squad may be expected from the normal recruit 
stream without special training. Unless present training sched- 
ules and methods are altered to permit improvement in marks- 
manship skill, this tends to set an upper limit on the number of 
highly skilled riflemen that it is feasible to assign to the squad 
from the standpoint of natural aptitudes available to the Army, 
and of the training effort. 

The figure(two experts per squad) is consistent, however. 



This does not mean that it would not be desirable to have much 
higher performance in marksmanship among all the men in the 
squad; the suggested assignments for experts merely empha- 
size the operational need for at least two experts per squad if 
training is unavailing in raising present standards of performance. 

It was not possible to obtain data from the AGO, "G-3, or OCAFF on the number of 
enlisted men who could be expected on the average to pass as experts. In private 
communication with Fort Benning, the Infantry School has indicated that about 10 
percent of the men receiving marksmanship training could be expected to pass as 
experts by known distance range firing standards. 



with that already given as the apparent actual requirement. 



32 




ORO-T-160 



To arrive with assurance at an optimum ratio, much more 
knowledge of small unit operations in combat would be required 
than is now known in ORO or elsewhere. Determinations at a 
"tactical laboratory, " such as ORO is eager to see established 
at Fort Benning, could contribute much to the solutions. 

Training 

The increases in effectiveness which have been proposed in 
this analysis all follow from innovations in design of the weapon 
for the purpose of overcoming deficiencies ip skill or training 
and for adapting the weapon to the nature of its actual opera- 
tional employment. Since there ia no reason to suppose that 
the new weapon would be char act eric ally unlike the present 
rifle in its method of operation, no increased demands for train- 
ing time or facilities are visualized. In fact, the short range 
of the weapon offers a chance for considerable reduction in 
weight and for less precision in working parts. Consequently, 
development of a lighter weapon, with low recoil, should facil- 
itate training in its use. 

Also, it is felt that men would react favorably to a weapon 
which increased their own marksmanship performance since 
it would add to their confidence in being able to hit the enemy 
at ranges where M-l rifle fire is comparatively ineffective. 

It does not seem reasonable to assume that a man's confidence 
in his weapon would be affected adversely by a design which 
increased his chances of hitting the enemy and therefore in- 
creased the probability of his own survival. 

In connection with present marksmanship training, the results 
given in the Appendix suggest strongly that considerable improve- 
ments are needed if skills are to approximate the precision capa- 
bilities of the M-l rifle. An examination of the current basic 
training program shows that 76 hours are allowed for marksman- 
ship training with the rifle, of which only 48 hours are involved 
in "wet" exercises, that is, actual range firing of the weapon. 17 

In the 48 hours of training, each man fires at least 400 rounds, 
which indicates roughly the total amount of time spent in the 
actual employment of the rifle. Any question of the adequacy of 
this training program could only be settled by field tests designed 
to determine the best methods and the time required to produce 
optimum results among men in their marksmanship skills. As 
shown in the Appendix, it is not likely that training alone could 
be effective in materially raising the standards of all men to 
exceed the level of expert performance indicated by the Belvoir 



ORO-T-160 




33 




tests. Significant gains in man -weapon effectiveness are to be 
obtained only by combining improvements in weapon design with 
good training. By the adoption of design principles in a hand 
weapon, as proposed in this study, an opportunity is offered to 
realize gains of considerable magnitude. 

Design Feasibility 

No insoluble problems appear to be involved in the engineering 
of a weapon possessing the recommended characteristics. To 
accomplish ideal dispersion in an automatic hand arm , as ideal- 
ized in the Appendix, many design difficulties will stand in the 
way of preserving desirable military characteristics such as 
lightweight, durability, reliability, automatic loading, and 
other factors. A salvo-type automatic which projected volleys 
of rounds to form the desired pattern at the range giving maximum 
hit effectiveness probably would represent the best type of design 
for deriving the greatest gains. This would entail designs which 
include the multi -barrel principle, high cyclic rate single-barrel 
types with a design feature for allowing the barrel to nutate at 
the muzzle on recoil for controlled dispersion, frangible missiles, 
aer ©dynamically controlled missiles, compensators, deflectors, 
and the like, all of which present a variety of engineering diffi- 
culties to be overcome before the weapon would function satis- 
factorily, The point of chief concern, however, is to strive for 
the attainment of the pattern dispersion principle so that the 
greatest possible gains can be derived, and in the striving, let 
the engineering difficulties argue for themselves. 

In studying the design problems, it was apparent that the 
smaller caliber weapon, with its bullets of smaller mass, would 
have considerably less recoil than present automatics, and that 
the reduced dispersion of a burst, along with the employment of 
a muzzle compensator, should have significant effects in reducing 
muzzle 11 walk -off. " As stated previously, it may well be that a 
light automatic of small caliber (in the region of .20 cal) would 
produce dispersions of rounds in short bursts which are not 
incongruous with the pattern dispersions specified in the Appendix. 
At least the tendency would be a significant reduction in dis- 
persion as compared to present automatics with their high recoil 
effects. Such reduction may be sufficient to regard the dis- 
persion as approaching the optimum requirements. 

Considering all factors, this approach to the problem appears 
to be straightforward, practical, and relatively simple, and it 
offers promise of fulfilling the desirable optimum dispersions 



£ : 






34 



ORO-T-160 




for maximum hit effectiveness. Tests on prototype models of 
new weapons of small caliber should be made to determine the 
practicality of this approach to the problem. 

A THEORY FOR DETERMINING 

RELATIVE EFFECTIVENESS OF DIRECT FIRE WEAPONS 

The analysis would not be complete if advantage were not 
taken of possible valuable theoretical applications which may 
be made using the two major parameters given in the analysis 
of the man-rifle system. These parameters relate to the prob- 
ability of seeing a man target on the battlefield and the probability 
of hitting the target with aimed fire. 

To test an hypothesis, according to which effectiveness might be 
evaluated, use was made of battlefield visibility data for the area 
of Korea where ranges were known for a small sample of rifle 
bullet hits among members of the Turkish Brigade. 

Method Used 

The method which has been used in estimating the expected 
distribution of hits as a function of range may be open to serious 
question because of the possible weakness of the assumptions 
made about actual rifle operations. Although the need was recog- 
nized for more adequate knowledge of the factors which exert a 
major influence on aimed rifle fire, it was felt that the data on 
visibility and hit probability might be useful for computing the 
expected distribution of hits as a function of range for different 
weapons. As shown in Table 1, the probability product of the 
hit data and of the visibility data for each range interval yields 
predictions on the relative distribution of hits, if one assumes 
expenditure proportional to targets seen and targets seen pro- 
portional to the map measurements on visibility. 

In Table 1, the data given for Ps are the fraction of all 
cases where a man can be seen continuously in the 50-yd inter- 
val. Employment of the data sets up a model which visualizes 
the enemy approaching a defender who fires on the enemy when 
he first appears. The results of the repetition of many cases 
of this simple dual situation should permit prediction of the 
type of distribution of hits as a function of range, for aimed rifle 
fire over the Korean terrain. While it is possible to calculate 
the number of hits to be expected as a function of range using 
column 4 of th er of hits cannot be 




ORO-T-160 



35 



: ORMATlON 



8 $ 



f > 

isV-Mi* 






I ^ 

r -rS-f'i | 

, ...... *.viUuOL. ww . , 

compared with the observed number because the sample of 
combat data did not provide information on the total number of 
men involved or the expenditure of rifle ammunition. For this 
reason, the percentage distribution of expected hits was com- 
pared to the observed distribution. 



TABLE 1 

COMPUTED DISTRIBUTION OF HITS AS FUNCTION OF RANGE R 



Range 
Interval, yd 


Ps a 


Ph b 


Ps x Ph 


Ps x Ph, 
Normalized 


Accumulated 
“Expected 
Fraction 
of Hits” 


0-49 


0.360 


1.00 


0.360 


0.457 


1.000 


50-99 


0.254 


0.93 


0.234 


0.297 


0.543 


100-149 


0.162 


0.76 


0.123 


0.156 


0.246 


150-199 


0.070 


0.54 


0.037 


0.047 


0.090 


200-249 


0.047 


0.38 


0.018 


0.023 


0.043 


250-299 


0.028 


0.28 


0.008 


0.010 


0.020 


300-349 


0.024 


0.22 


0.005 


0.006 


0.010 


350-399 


0.016 


0.17 


0.003 


0.004 


0.004 


Totals 






0.788 


1.000 





^Probability of seeing target within each interval. 
Probability of hit- 



In Fig. 6, the distribution for the calculated fraction of hits 
corresponds roughly with the distribution of actual hits in com- 
bat in Korea. 

As a matter of interest, the M-l rifle and the five-round 
salvo type weapon were compared in this way for the two extreme 
types of terrain, Class A and Class C. The expected distribution 
for hits from both weapons at ranges greater than R for the 
Korean terrain and for the Normandy terrain is given in Fig. 7. 
Since these distributions do not show the relative effectiveness 
of the two weapons, the same model was used to provide an 
indication of the merits of the salvo weapon over the rifle as 
terrain influences effectiveness. 

In this instance, as shown in Table 2, the hits were calculated 
on the basis of 100 shots fired for each weapon at man targets 
distributed over terrain in accordance with the distribution given 
for Ps. 



36 




ORO-T-160 



5ECURI 



'ION 



PROBABILITY OR FRACTION 




r 










0 100 200 300 400 500 



R- RANGE (YD) 

Fig. 6 — Rifle marksmanship, battlefield visibility, and hit probability in 
combat. A: Ph, probability of hitting man-target as function of range; 
B, observed fraction of hits occur ing at ranges greater than R; C, proba- 
bility of seeing target at ranges greater than R(l-Ps); D, computed frac- 
tion of hits expected to occur at ranges greater than R(Ps x Ph, where 
Ps is converted to frequency of visible areas occuring in each 50 yd 
interval, and where Ph is averaged in each interval by assuming the 
mean P value). 

* Assumes expenditure proportional to targets seen and targets seen proportional 
to Ps. 



ORO-T-160 




m 




INFORM? 



SECURITY 



HIT PROBABILITY 



s ulum i i u t m r mmmmm 

A 



t yrt, r* J fy f* - 1 

j> f 1 




Fig. 7 — Theoretical distribution of hits as function of range for M-l Rifle and a Salvo- 
Type Hand Weapon for Class "A” and *‘C” Terrains. 



TABLE 2 

RELATIVE EFFECTS OF M-l SINGLE-ROUND FIRE AND SALVO FIRE 
AS FUNCTION OF RANGE FOR TERRAIN TYPES A AND C 



Range 
Interval* yd 


Ps a 


Ph b 


Expected Hits 


Ps x Ph, 
Normalized 


Class A 


Class C 


M-l 


Salvo 


M-l 

Glass A 


Salvo 
Class A 


M-l 

Class C 


Salvo 
Class C 


0-49 


0.360 


0.05 


1.00 


1.00 


37 


37 


9 


9 


50-99 


0,254 


0.10 


0.93 


0.99 


24 


26. 


16 


17 


100-149 


0.162 


0.09 


0.76 


0.96 


12 


16 


12 


15 


150-199 


0.070 


0.09 


0.54 


0.89 


4 


6 


8 


14 


200-249 


0.047 


0.09 


0.38 


0.81 


2 


4 


6 


12 


250-299 


0.028 


0.06 


0.28 


0.71 


1 


2 


3 


9 


300-349 


0.024 


0.06 


0.22 


0.60 


1 


1 


2 


6 


350-399 


0.016 


0.04 


0.17 


0,49 


0 


1 


_1 


3 


Totals 


0.961 


0.58 






81 


93 


57 


85 



^Probability of seeing target within each interval 
■'probability of hit. 



38 



assiti 

mm mm 



ORO-T-160 



100 



100 




80 — N 




\ 

\ 



\ 

\ 

\ 



CLASS C TERRAIN 



(Normandy) 



0 



100 



200 



300 



400 



0 



100 



200 



300 



400 



RANGE (YD) 



Fig. 8 — Relative effectiveness of M-l Rifle and Salvo Automatic for Class "A" and 

"C” Terrains. 



It will be noted in Fig. 8 that the comparative effectiveness 
of the salvo weapon is much greater for open terrain types like 
Class C than for terrain types of Class A because of the greater 
hit effectiveness of the salvo weapon at the longer ranges. Such 
information, although only relative, suggests that the dispersion 
type hand weapon would offer material advantages over the M-l 
rifle in areas of combat such as western Europe. On the other 
hand, the advantages of the new weapon in areas like Korea are 
not as great and the comparison made in Fig. 8 supports the 
contention that a hand weapon designed for semiautomatic use 
in the short ranges and for full automatic use in the longer 
ranges with controlled dispersion would offer a good solution 
for the common hand arm. 

If theory, as herein presented, can be confirmed by more 
extensive knowledge of expenditure and ranges of hits incurred 
in combat by the rifle and other direct fire weapons to include 
machine guns, recoilless rifles, antitank weapons, and the 
like, the method would constitute a promising basis for eval- 
uating a balanced weapons system, and T/O&E for units might 
be established on a quantitative basis. 




ORO-T-160 



39 



f, ? r*- - 



CONCLUSIONS 



1. The ranges at which the rifle is used most frequently in 
battle and the ranges within which the greater fraction of man 
targets can be seen on the battlefield do not exceed 300 yd. 

2. Within these important battle ranges, the marksmanship 
of even expert riflemen is satisfactory in meeting actual battle 
requirements only up to 100 yd; beyond 100 yd, marksmanship 
declines sharply, reaching a low order at 300 yd. 

3. To improve hit effectiveness at the ranges not covered 
satisfactorily in this sense by men using the M-l (100 to 300 
yd), the adoption of a pattern-dispersion principle in the hand 
weapon could partly compensate for human aiming errors and 
thereby significantly increase the hits at ranges up to 300 yd. 

4. Current models of fully automatic hand weapons afford 
neither these desirable characteristics nor adequate alternatives. 
Such weapons are valueless from the standpoint of increasing 
the number of targets hit when aiming on separated man- size 
targets. 

5. Certain of the costly high standards of accuracy observed 
in the manufacture of current rifles and ammunition can be relaxed 
without significant losses in over-all hit effectiveness. 

6. To meet the actual operational requirements of a general 
purpose infantry hand weapon many possibilities are open for 
designs which will give desirable dispersion patterns (and accom- 
panying increases in hit probability) at the ranges of interest. Of 
the. possible salvo or volley automatic designs, the small caliber, 
lightweight weapon with controlled dispersion characteristics 
appears to be a promising approach. (Low recoil of a small cal- 
iber weapon facilitates dispersion control. ) 

7. To create militarily acceptable wound damage at common 
battle ranges, missiles of smaller caliber than the present stand- 
ard .30 caliber can be used without loss in wounding effects and 
with substantial logistical and over -all military gains. 

8. A very great increase in hit lethality can be effected by 
the addition of toxic agents to bullet missiles. 



RECOMMENDATIONS 



1. It is recommended that the Ordnance Corps proceed to 
determine the design or technological feasibility of developing a 



ORO-T-160 




>N 



f j 3 ft ^ i s ** 1 1 1 *h : i i 
w i iv3 wty wiliiry 

hand weapon which has the characteristics cited in this analysis* 
namely: 



a. Maximum hit effectiveness against man targets within 
300 yd range. (This does not mean that the weapon will be ineffec- 
tive beyond this range. ) 

b. Small caliber (less than .30). 

c. Wounding capability up to 300 yd at least equivalent to 
the present rifle. 

d. Dispersion of rounds from salvos or bursts controlled 
so as to form a pattern such that aiming errors up to 300 yd will 
be partly compensated, and hit effectiveness thereby increased 
for these ranges. 

2. As one possible alternative to the current "volume of fire" 
(fully automatic) approach to the problem of increasing the effec- 
tive firepower of infantry riflemen, it is recommended— subject 
to tentative confirmation of design feasibility— that a rifle incor- 
porating at least in principle the military characteristics here 
proposed be manufactured for further and conclusive test. 



ORO-T-160 




41 



lATION 



BIBLIOGRAPHY 





1. Gardner, John H. ; Hitchman, Norman A.; Best, Robert J, 

ORO-R-5: ALCLAD Final Report, Appendix A. 

1 August 1951 (SECRET). 

2. Johnson, Ellis A.; Parker, Edward M.; and ORO Staff. 

ORO-R-3: MAID Report , Appendix H. 

21 January 1950 (SECRET). 

3. ORO-R-5, Appendix B (SECRET). 

4. DeBakey, M. and Beebe, G. Battle Casualties. Springfield, 

Illinois: C. Thomas Co., 1951 (UNCLASSIFIED). 

5. Oughterson, Col. A. W. Wound Ballistics Report , 

Bougainville Campaign, 1944 (RESTRICTED). 

6. Office of the Surgeon General, Wound Ballistics Survey , 

Korea (15 November, 1950-5 May 1951) (CONFIDENTIAL). 

7. AORG liaison Letter, December 1951 (SECRET). 

8. Donovan, Grace N. ORO-T- 18{FEC): Use of Infantry Weapons 

and Equipment in Korea . August 1952 (SECRET). 

9. Kaye, J. D. The Use of Infantry Weapons in Korea . 

ORS/Korea. Report No. 6, 12 March 1952 (SECRET). 

10. Bayly Pike, D. F. and Goepel, Charles. ORO-T-161: The 

Effects of Terrain on Battlefield Visibility (SECRET). 

11. Army Field Forces. Report of Board No. 3, Project 2231 , 

Vols. I and II. Fort Benning, Georgia, 27 October 1950 
(SECRET). 

12. National Research Council. Missile Casualty Reports , 

Nos: 1 to 17. 

13. Chemical Corps Medical Laboratory, Wound Ballistics of 

a .22 Caliber Brass Scale Model of the .30 Caliber M-2 
Rifle Ball , Research Report No. 94, December 1951 
(CONFIDENTIAL). 

14. Hall, D. L. An Effectiveness Study of the Infantry Rifle , 

BRLM 593, March 1952 (CONFIDENTIAL). 

15. Army Chemical Center. Reports on Project 4-04-19-001 

(SECRET). 

16. ORO unpublished Study. 

17. FM-23-5, US Rifle Cal .30 M-l, October 1951 (UNCLASSIFIED). 




42 



ORO-T-160 



sisuKT^5Erin!^®®^fr oN 



f 






i 




APPENDIX 

ANALYSIS AND APPLICATION OF 
RESULTS OF RIFLE-RANGE TESTS 



V 






IN 



? £% i 



i iUi 



APPENDIX 



ANALYSIS AND APPLICATION 
OF RESULTS OF RIFLE-RANGE TESTS 

CONTENTS 





Page 


SUMMARY 


49 


INTRODUCTION 


49 


ANALYSIS 


50 



Objective — Data from Tests — Determination of 
Means (mpi) and Dispersion (Standard Deviation) — 
Summary of Means and Standard Deviation — Disper- 
sion as a Function of Range — Systematic Errors in 
the mpi — Comparison of Observed and Theoretical 
Distributions of Deviations from mpi — Remarks on 
the Homogeneity of Results for Individual Riflemen — 
Remarks on Deviations of mpi from Aiming Point — 
Comparison of Observed and Theoretical Probabilities 
of Hitting Target at Various Ranges — Remarks on 
Results of Firing on Targets Appearing Randomly at 
Either of Two Ranges. 

APPLICATION 91 

Theoretical Probability of Hitting Type E Silhouette 
Target With a Salvo Pattern — Probabilities for 1,2, 

3,4, and 5 Hits on Man-Size Target With Five-Shot 
Pattern Salvo — Comparison of Theoretical Probabil- 
ities of Hitting “Average Target" with Single -Shot 
and Five-Shot Pattern Salvo — Remarks on Significance 
of Probabilities of Hitting a Target with a Single-Shot 
and with Five-Shot, Four -Shot Pattern Salvos — Effect 



ORO-T-160 45 



IN 



Page 



^rvPI 






t > 



1 it* on 



CONTENTS (Continued) 



of Weapon Dispersion on Probability of Hitting 
Target. 



FIGURES 

A1-A32. Shot Patterns on Target and Screen, Tests 
1 and 2. 



A33. Example illustrating use of probability paper 
to determine standard deviations and means, 
whether or not distribution is truncated 

A34. Observed standard deviation, S r , of distance 
of individual shots from mpi as function of 
target range, for experts 

A35. Observed standard deviation, S r , of distance 
of individual shots from mpi as function of 
target range, for marksmen 

A36. Distance of mpi from top of target as function 
of range 

A37. Distance of mpi from vertical line through 
target center as function of range; Test 1 

A38. Distance of mpi from vertical line through 
target center as function of range; Test 2 

A39. Probability of expert riflemen hitting Type E 
silhouette of range 

A40. Probability of marksmen hitting Type E silhou- 
ette target as a function of range 

A41. Probability of hitting Type E silhouette target 

with single shot compared with probability of at 
least one hit with a five -shot pattern salvo; 
curves based on aiming errors 




ORO- 



75 

76 
78 

80 

84 

85 

86 
88 
89 

92 

-160 



Imation 









FIGURES 


CONTENTS (Continued) 


Pag 


A42. 


Probability of hitting “average" target. A, 
with single shot compared with probability 
of at least one hit on target with five-shot 
pattern salvos. 


94 


A43. 


Probability of hitting a circular target as 
function of range for several weapon-ammu- 
nition errors 


97 


TABLES 

AI. 


Rifle Range Test 1 


98 


A2. 


Rifle Range Test 2 


99 


A3. 


Rifle Range Test 3 


100 


A4-5. 


Comparison of Observed Number of Shots 
Inside Zones Bounded by Circles of Radii 
r i and ^ in., with Number Expected from 
Bivariate Distribution with Radial Standard 
Deviation a r , at four Ranges, R, in yd. 

Test 1 (Ei and Es) 


101 




Test 1 (Mi and Ms) 


102 


A.6-7. 


Comparison of Observed Number of Shots 
Inside Zones Bounded by Circles of Radii 
r^ and r ^ in., with Number Expected from 
Bivariate Distribution with Radial Standard 
Deviation <7 r , at four Ranges, R, in yd. 

Test 2 (Ei and Es) 


103 




Test 2 (Mi and Ms) 


104 


A8. 


Probabilities for Experts Firing Individually, 
of Obtaining Exactly 1, 2, 3, 4, and 5 hits on 
Type E Silhouette with Five -Shot Pattern 
Salvo for Indicated Target Ranges 


105 


A9. 


Probabilities for Marksmen Firing Indi- 
vidually, of Obtaining Exactly 1, 2, 3, 4, and 
5 Hits on Type E Silhouette with Five -Shot 
Pattern Salvo for Indicated Target Ranges 


105 



ORO-T-160 



47 



TARGET RANGE DIAGRAM 





Therange area can be described as a common- looking open-field area with gentle undulations 
in the ground and with heavy grass, shrubs, and the like covering the surface area as one 
would see in relatively open country in many parts of the world. 



48 




ORO-T-160 



SiCURl 



lTION 



p 



* fl** 

BV1 

d E s 



i \J 



SUMMARY 



Results of expert riflemen and marksmen firing at man- size 
targets at different ranges were analyzed to determine aiming 
errors as function of range. The aiming errors in mils were 
found to be independent of range. Results of the analysis were 
used to compute the probability of hitting targets smaller than 
the man-size target and, therefore, more realistically repre- 
sentative of the average area presented by men in combat. 

Results of the analysis were also used to predict the probabilities 
of hitting targets with a hypothetical weapon firing a five -shot 
pattern and a four -shot pattern salvo. The probability of obtain- 
ing at least one hit from a single -salvo firing was found to be 
decidedly greater than the probability of hitting with a single -shot 
weapon. Probabilities of obtaining multiple hits with the salvo- 
weapon were also computed. Finally, the effect of weapon disper- 
sion on the probability of hitting was determined. These com- 
putations show that eliminating the weapon- ammunition disper- 
sion would not materially improve the rifleman's hit probability. 



INTRODUCTION 

In the BALANCE study of the Army weapons system, examination 
of the basic hand arm of the infantry, the rifle, indicated a need to 
study the effectiveness of aimed rifle fire on man-size targets at 
ranges of combat interest. Heretofore, marksmanship has been 
measured by scoring hits on target only, and sufficient evidence could 
not be obtained on the nature of the dispersion (magnitude of errors) 
of all rounds fired. 

To provide basic parameters for the whole rifle study, a field test 
was conducted at Fort Belvoir, Ya. , where expert riflemen and 
marksmen were used in a series of experiments designed to provide 
data from which meaningful conclusions could be drawn. Two grades 
of riflemen (expert and marksman) were used so that by Army 
standards the upper and lower limits of marksmanship could be 
studied. By having the men fire on man- silhouette targets (type E) 
at battle ranges of 100-300 yd on a transition type range, an element 
of combat realism was provided. In order to record and measure 
the dispersion of rounds, target screens 6 ft high and 12 ft wide 
were mounted behind the silhouette target at each range. The 
Appendix Frontispiece shows the design of the range used and the 
manner in which targets were located. 



ORO-T-160 



49 



" Mini 1 1 ^fON 




Dimensions of the screens and test procedures were products 
of preliminary trials designed to determine the methodology and 
physical requirements necessary to study the man-rifle complex 
on the desired basis. The target butts were draped with OD target 
cloth so that rounds below the target and screen could be taken into 
account by the perforations made in. the cloth. The target cloth also 
was useful in camouflaging the mounds of earth at each target 
location. 

In the test plan, psychological factors which might have arisen 
in group firing were eliminated by arranging groups of experts and 
marksmen with equal representation on the fire line. Also, to 
remove any learning effects in the experiment, the order of fire on 
targets was arranged in a manner to follow a latin square type of 
plan. This plan allowed each man to complete his firing serial on 
four ranges by ending the serial on the target with which he had 
begun, making a total of five target shoots on four ranges. Learn- 
ing was not found to be a significant variable, and is not included 
in the analysis. 

Test personnel were selected according to marksmanship scores 
from 13 training companies in the Engineer Replacement Training 
Center, Fort Belvoir, Va. Sixteen riflemen (eight experts and eight 
marksmen) were used on each of the two tests yriiich were conducted 
on different days. Since different men were used in each test, a 
total of 32 men were employed in the whole experiment. The follow- 
ing outline shows the variety of conditions studied and the plan of 
tests. The shots on target and screen were color-coded in each 
experiment to make identification possible. All firing was done from 
the prone position using M-l rifles and battle sights. 

ANALYSIS 

Objective 

The objective of the analysis was to determine accuracy 
of aimed rifle fire, and its dependence on target range, for 
marksmen and experts firing the M-l rifle under the conditions 
previously described. The accuracy thus obtained was required 
as a basis for predicting with reasonable reliability, the 
results which might be obtained with a hypothetical weapon of 
comparable accuracy which could fire several bullets in a pre- 
determined pattern. 

Data from Tests 

The locations of bullet holes, derived from the tests are 



50 




ORO-T-160 



SECMfff 4HHf 



PLAN OF RIFLE MARKSMANSHIP TESTS 
Fort Belvoir, Va., 27 Oct and 10 Nov 1951 



Plan of Testa 1 and 2 



Purpose 


Subject 


Order of Fire 


Conditions 


To evaluate 


E 


A-B-C-D-A 


Targets (silhouettes) exposed for 3 sec 


individual 


M 


C-D-A-B-C 


every 3 sec. For each exposure, each man 


marksmanship 


E 


B-A-D-C-B 


fired one round; 8 rounds fired per man per 




M 


D-C-B-A-D 


target. Firing done in 4-man serials. 




E 


A-D-C-B-A 


Conditions repeated. 




M 


B-C-D-A-B 






E 


D-A-B-C-D 






M 


C-B-A-D-C 






E 


A-B-C-D-A 


Conditions repeated. 




M 


C-D-A-B-C 






E 


B-A-D-C-B 






M 


D-C-B-A-D 






E 


A-D-C-B-A 


Conditions repeated. 




M 


B-C-D-A-B 






E 


D-A-B-C-D 






M 


C-B-A-D-C 




To evaluate 


8 


B-A-D-C-B 


Target exposed for 3 sec every 3 sec. 


group 


experts 




Group fired simultaneously at each range, 


marksmanship 






single round firing for each exposure, 4 
rounds per target per man. 




8 


B-A-D-C-B 


Same conditions as for experts. 




marksmen 






Test No. 3 


To study 


4 


C-A-C-C-A-A-C-A 


Targets exposed for only 1 sec, alternate 


effects of 


marksmen 




snap shooting at two target ranges, 


rapid fire 






schedule of exposure shown was unknown 


when order of 






to the men. Experiment was done for 


target 






group or simultaneous firing and for 


appearance 
is unknown 






individual firing. 




4 


C-A-C-C-A-A-C-A 


Same as above conditions. 




experts 







KEY 



E Expert 
M = Marksman 
A ■= Tgt at 110 yd 



3 = Tgt at 205 yd 
C = Tgt at 265 yd 
D = Tgt at 310 yd 



ORO-T-160 



51 



INCHES 



— ■if-™ tE(gFT^iiaHtittai» 

[. | „ ^ f „ 

I >. 

shown in Figs. A1 to A3Z, on which are also indicated the num- 
ber of shots which were fired and the number of these which hit 
the screen. In most of the tests, some of the rounds did not hit 
the screen. Most, if not all, of these were observed to have hit 
the ground in front of the screen. While the percentage of shots 
hitting the target, as tabulated in the last column of Table A1 is, 
of course, a function of accuracy, it does not provide complete 
information on the nature of the dispersion of the shot -pattern. 




Fig. Al— 110 yard range (Test No. 1), expert riflemen firing individually, 96 rounds fired 
(8 each by 12 men), 96 rounds on target cloth, 88 rounds on target 





> ft 



i v 



SECIIBIIiM(C(B£LttSS&» AT10N 



52 



ORO-T-160 



-160 ORO-T-160 




6 

z 




o 

O- 







ui 




Fig. A2 — 205 yd range (Test No. 1), expert riflemen firing individually, 80 rounds fired (8 each by 10 

men), 69 rounds on target cloth, 36 rounds on target 



Unctenr» 




Fig. A3— 265 yard range (Test No. 1), expert riflemen firing individually, 72 rounds fired (8 
each by 9 men), 62 rounds on targer cloth, 34 rounds on target 




Fig. A4 — 310 yard range (Test No. 1), expert riflemen 
firing individually, 72 rounds fired (8 each by 9 men), 
47 rounds on target cloth, 28 rounds on target 




54 



ORO-T-160 



INI 



J 

*0 50 



ids fired (8 




Fig. A5 — 110 yard range (Test No. 1), expert riflemen firing simultaneously, 32 rounds fired 
(4 each by 8 meri), 24 rounds on target cloth, 20 rounds on target 



-T-160 



« 

ORO-T-I60 



55 



seMh SECIW THformatRW 




securi 



INFORMATION 




|s 8( 



’•j 




Fig. A6— 205 yard range (Test No. 1), expert riflemen firing simultaneously, 32 
rounds fired (4 each by 8 men), 26 rounds on target cloth, 12 rounds on target 



1 rt f" 4 * s 



inrijis 



j t, vjt t y 






Qlliu 



56 



ORO-T-160 



iTION 



51 



MCMt 



ION 




usty, 32 
target 






Fig. A7 — 265 yard range (Test No. 1), expert riflemen firing 
simultaneously, 32 rounds fired (4 each by 8 men), 21 rounds 
on target cloth, 11 rounds on target 




Fig. A8 — 310 yard range (Test No. 1), expert 
riflemen firing simultaneously, 32 rounds 
fired (4 each by 8 men)^ 19 rounds on target 
cloth, 9 rounds on target 




INCHES 



40 




pi ,, 110 yard range (Test No. 1), marksmen firing individuolly, 56 round. fir^ (8 ooch by 7 n.on) - 8 round. 

Fig. A9— 1 in y«d '«9« l • round, on turgor dolk, 39 round, on turgor 



u 

I 



o 



30 



20 



10 



10 



20 



INCHES 



Fig. A9 110 yard rang© (Test No. 1), marksmen firing individually, 56 rounds fired (8 each by 7 men) -8 rounds 

fired by Bates not included-56 rounds on target cloth, 39 rounds on target 



O 

V 

O 

H 



O' 

o 





Fig* A10— 205 yard range (Test No. 1), marksmen firing individually, 72 rounds fired (8 each by 9 men), 58 rounds 

on target cloth, T9 rounds on target 



<ji 

\D 



SECURITY 



SECURITY 



INFORMATION 



piper 

luOoj 



iO 



* K 

iTiprf 

! I a %uil 




Fig. All 265 yard range (Test No. 1), marksmen firing individually, 72 rounds 

fired (8 each by 9 men), 65 rounds hit target cloth, 25 rounds hit target 




Fig. A12 310 yard range (Test No. 1), marksmen firing 

individually, 80 rounds fired (8 each by 10 men) -Bates 
excluded, 61 rounds on target cloth, 24 rounds on target 



i tvi ft 

uIaSo!ll0( 



60 



ORO-T-160 



RATION 



ORO-T-160 



I 

H 

t 

I—* 

o 

© 



flu 



J L 



J L 




Fig. A13 — 110 yard range (Test No. 1), marksmen firing simultaneously, 32 rounds fired (4 each by 8 men), 30 rounds hit target cloth, 

12 rounds hit target 



WMATION 



ORO-T-160 




r 



Fig* A14 — 205 yard range (Test No. 1), marksmen firing simultaneously, 32 rounds fired (4 each by 8 meni 

19 rounds on target cloth, 4 rounds on target 



mm 






w 



i /r* f 

! . Nl 




Fig. A15— 265 yard range (Test No. 1), marksmen firing simultaneously, 32 rounds fired (4 each by 
8 men), 32 rounds hit target cloth, 6 rounds hit target 




Fig. A16 — 310 yard range (Test No. 1), marksmen firing simultaneously, 
32 rounds fired (4 each by 8 men), 25 rounds hit target cloth, 4 rounds 
hit target 



ORO-T-160 



63 










Fig* AI7 — 110 yard range (Test No* 2), expert rifletnen firing individually, 96 shots fired 
(8 each by 12 men), 91 rounds hit target cloth, 81 rounds hit target 



64 



pH 1 




ORO-T-160 



IATION 





Fig. A18 — 205 yard range (Test No. 2), experts firing individually, 64 rounds fired 
(8 each by 8 men), 45 rounds hit target cloth, 22 rounds hit target 



ORO-T-160 




65 



SECI 



INCHES INCHES 






INFO'Ri 




Fig. A19 — 265 yard range (Test No. 2), expert riflemen firing 
individually, 64 rounds fired (8 each by 8 men), 56 rounds on 
target doth, 30 rounds on target 




Fig. A20 — 310 yard range (Test No. 2), expert riflemen firing 
individually, 80 rounds fired (8 eoch by 10 men), 77 rounds hit 
target doth, 35 rounds hit target 



66 



ORO-T-160 



ION 



iMATION 



* 





Fig. A21 — 110 yard range(Test No. 2), experts firing simultaneously, 32 rounds fired (4 each 
by 8 men), 28 rounds hit target cloth, 28 rounds hit target 




n r* I o o c* ifi £j i 
I ii/lQwOli IbU 



ORO-T-160 



67 



ORO-T-160 



CD 




\ 



Fig. A22 — 205 yard range (Test No. 2), experts firing simultaneously, 64 rounds fired (4 each by 16 men), 

58 rounds hit target cloth, 19 rounds hit target 




Fig. A23 — 265 yard range (Test No. 2), expert riflemen firing 
simultaneously, 32 rounds fired (4 each by 8 men), 28 rounds 
on target cloth, 13 rounds on target 




Fig. A24 — 310 yard range (Test No. 2), expert riflemen firing 
simultaneously, 32 rounds fired (4 each by 8 men), 25 rounds 
hit target cloth, 8 rounds hit target 




ORO-T-160 



69 



INCHES 



m 



TION 




Fig. A25 — 110 yard range (Test No. 2), marksmen firing individually, 64 shots fired (8 each 
by 8 men), 64 rounds hit target cloth, 34 rounds hit target 



70 



GRO-T-160 



ATION 



09 t-l-o*o 



1 



1 



1 



1 




Fig* A26 — 205 yard range (Test No. 2 ), marksmen firing at target individual ly, 72 rounds fired (8 
each by 9men) / 59 rounds hit target cloth, 12 rounds hit target 



INFORMATION 



10 



0 



30 



20 



10 



0 



10 



20 



30 



40 



50 



60 



70 



INCHES 

Fig, A27 — 265 yard range (Test No. 2), marksmen firing individually, 96 rounds fired 
(8 each by 12 men), 88 rounds on target cloth, 19 rounds on target 



30 20 10 0 10 20 30 40 50 60 70 

INCHES 

Fig, A28 — 310 yard range (Test No. 2), marksmen firing 
individually, 80 rounds fired (8 each by 10 men), 61 rounds 
hit target cloth, 12 rounds hit target 



70 



60 



50 




K 40 



20 



10 



0 



72 





SEC 






poi* 



by 16 men) - 1 man fired 5 rounds -49 rounds hit targetcloth, lOrounds hit 





Fig. A31 — 265 yard range (Test No. 2), marksmen firing 
s imultaneous I y f 32 rounds fired (4 each by 8 men), 24 
rounds hit target cloth, 8 rounds hit target 




Fig. A32 — 310 yard range (Test No. 2), marksmen firing 
simultaneously, 32 rounds fired (4 each by 8 men), 26 rounds 
hit target cloth, 2 rounds hit target 



ORO-T-160 



75 



x (IN.) 




and Dispersion (Standard Deviation) 

As already indicated, the location of those rounds which did 
not hit the target or screen, is, of course, unknown. How then 
can the mean (mpi) and dispersion (standard deviation) be deter- 
mined when these depend on the actual location of all shots? This 
problem is most conveniently solved by using probability paper as 
illustrated in Fig. A33. 



STANDARD DEVIATION (OR MEANS) LESS THAN THAT INDICATED BY ORDINATE, % 

Fig. A33 — Example illustrating use of probability paper to determine standard deviations 
and means, whether or not distribution is truncated. Data are from Test 1, experts firing 
individually at 205 yd. 

Suppose x is a variable normally distributed about mean x, 
and suppose from a sample of n x's F, is determined, where F t 
is the fraction of all the x's in the sample which have values less 
than x t , and F, the fraction containing all values of x less than 
Xj (x t >> x t )and so on to F n . Then for a normal distribution of the 
x's, the scale of F (abscissa scale of Fig. A33) is so designed 
that when values of F are plotted against the corresponding x , 
the points determine a straight line. The ordinate, on this line, 
corresponding to abscissa F =50 (i. e. , 50 percent) determines 



60 




.01 o.i 



5 10 20 30 40 50 60 70 80 90 95 98 99 99.9 99.99 



76 






ORO-T-160 




y (IN.) 



r 



the mean of the sample. If this mean is subtracted from the 
ordinate corresponding to abscissa F = 0.841, the difference is 
the estimated standard deviation of individual values about the 
mean of the sample. 

Thus, the upper line in Fig. A33 indicates mean: x = -0.5 inch 
and standard deviation: S x = 13.5 in. These apply to the x coordinates 
of the points of Fig. A2. Similarly from the lower line in Fig. A33: 
y = 16.0 inches (y measured from bottom of screen in Fig. A2) and 
S y = 15.0 inches. The percentages (i. e. , abscissae) for the points 
along the lower line of Fig. A33 were computed using as base (i. e. , 
100 percent) the total number of shots fired (i. e. , 80 from Fig. A2), 
although of these (11/80) 14 percent were off the screen at the 
bottom. Thus, even though the distribution of y ' s is truncated at 
y - o (bottom of screen), it is relatively simple to estimate the 
mean and the standard deviation through the use of probability paper 
which incidently facilities the calculation even for the nontrun- 
cated case. 

On the other hand, if the distributions of x and y are statistically 
independent (as was the case of Fig. A1 for which the correlation 
between x and y did not significantly differ from zero) then, refer- 
ring to Fig. A2, the mean and standard deviation of x will be 
independent of y. Hence, in computing the percentages (ordinates) 
for the upper set of points in Fig. A33, it was essential to use a 
base (i. e. , 100 percent) equal to the number of shots on the screen 
(i. e. , 69 from Fig. A2). That is to say, the distribution of the 
x’s of Fig. A2 is not truncated, as was that of the y’s; only the 
sample size for x is diminished as a consequence of some 11 
shots having gone off the screen. 

Summary of Means and Standard Deviation 

Proceeding as described in the preceding paragraph, the means 
of x and y and their standard deviations were determined for each of 
the test results shown in Figs. A1 to A32. For Tests 1 and 2, the 
results are given respectively in Tables A1 and A2. Inspection 
of S x and Sy(i. e. , the standard deviations of x and y) in Tables 
A1 and A2 indicates on the whole no very great difference between 
S x and Sy . More elaborate tests indicate the same conclusion. 

For example, in Test 1, Table 1, if S x and Sy in the first four 
rows are each normalized to range 100 yd (on the assumption of 
constant mil error), and then the variance of x and y are sepa- 
rately pooled (from the results at the four ranges), the resulting 
S x = 4.9 inches and S y = 5.8 inches, a difference of only 18 per- 
cent. In other cases, for example, in Test 1 for marksmen 



ORO-T-160 



77 



iILPJ 



t Jf O Q ( T f p W 

firing individually, (M,, Table Al) S exceeds S . Hence, on the 
whole no serious consequences are likely to arise from assuming 
°x = a y * or the results (a x , and <r y are standard deviations for 
the whole population). 




Dispersion as a Function of Range 

In the preceding paragraph, it was indicated that when the 
standard deviation in x (or y) at each of the four ranges was 
divided by the range, the results were essentially independent 
of range. It was also indicated that x and y were independent 





Fig. A34— -Observed standard deviation, S r , of distance of individual 
shots from mpi as function of target range, for experts. °, Test 1; +, 
Test 2; I, centered at from combined results of Tests 1 and 2. 
Total vertical extent of 1 indicates range within which 50 percent of 
results from similar samples should fall. 





1 * 1 


\ p n 




fr <4 Li .. 


L [ P. 



78 



ORO-T-160 



(i. e. . correlation zero) and that their standard deviations could 
be assumed equal. This suggests the standard deviation of 
r (r* = x 2 + y J ) as a convenient measure of dispersion since it 
combines S x and S y (actually S r * = S y J + S x a ). 

For Tests 1 and 2 respectively, values of S r are listed in 
column 7 of Tables A1 and A2. In Figs. A34 and A35, these 
values of S r are plotted as a function of range to target. It is 
evident in Figs. A34 and A35 that the "observed" values of 
for the different ranges are, within the indicated statistical 
uncertainties, reasonably approximated by the indicated straight 
lines. This implies that the dispersion (standard deviation) in 
inches at the target increases linearly with the target range, 
according to the equations indicated. The constants show that, 
in accuracy, the riflemen rank in the following order: (1) experts 
firing individually, (2) experts firing simultaneously, (3) marks- 
men firing individually, and (4) marksmen firing simultaneously. 



Systematic Errors in the mpi 

Figure A36 indicates the vertical distance of the mpi from 
the top of the target, at the four ranges, for experts and marks- 
men in Tests 1 and 2. Even if all men aimed at the center of 
the target, vertical systematic deviations of the mpi from the 
aiming point would be expected as a consequence of the parabolic 
nature of the bullet trajectory. How the vertical coordinate of 
the mpi varies with range would depend on the range for which 
the sights are set. Figures A37 and A38 indicate for Tests 1 
and 2, respectively, the x - coordinate of the mpi at different 
ranges. It is evident that in Test 1 the bias is quite small' and 
in most cases probably not statistically significant. On the 
contrary, the bias in Test 2 is generally larger than in Test 1, 
particularly for marksmen, and is in many cases statistically 
significant. Results of tests for the significance of this bias are 
given in the last row of Tables A4, A5, A6, and A7, on which 
further comment will follow. 



Comparison of Observed and 

Theoretical Distributions of Deviations from mpi 

If x and y are deviations from a mean, and are independently 
and normally distributed with equal standard deviations, a x = a , 
then it is convenient to consider the distribution of radial y 
deviations, r, ^(r = x + y ), which have standard deviation, 

°r = (°x* + CT y*)^- 14 can be shown that, of all the radial deviations 



ORO-T-160 



79 



INCHES INCHES 



flwwSECItlT 




0 100 200 300 400 



RANGE (YD) 




Fig. A35 — Observed standard deviation, $ r , of distance of individual 
shots from mpi as function of target range for marksmen. For meaning 
of symbols see Fig. A34. 



80 



ORCUT-160 



from the mean, the fraction having deviations greater than or 
equal to kv r is, on the average, given by: 

W(k) = e (1) 

or looked at in another way W(k) is the probability that a shot 
falls outside the circle of radius r = kt7 r . The following table 
indicates values of W(k) for a few selected values of k: 



k 


0.000 


0.536 


0.833 


1.179 


DO 


W (k) 


1.000 


0.750 


0.500 


0.750 


0.000 



In particular, the circle of radius 0.833 a r , with W(k) = 0.500, 
is usually called the circular probable error (cpe). Thus circles 
of radii, o, 0.536 a r , 0.833 a T , 1.179 a r , and «, with centers at 
the mpi, divide the plane into four zones, such that the proba- 
bility of a shot hitting within any one of the zones is 25 percent. 
These circles were drawn in each of the originals of Figs. A1 
to A32, (but they are not reproduced here), and the radii of the 
circles bounding each zone are listed in Tables A4, A5, A6, 
and A7. These tables also indicate the expected and observed 
numbers of shots falling in each zone. 

In several cases, such as illustrated in Fig. A4, parts of some 
or of all zones are off the screen. For these cases it is obviously 
impossible to indicate how those shots which did not hit the screen 
were distributed among the zones. In such instances only those 
shots observed to hit the screen can be properly allocated among 
the partial zones which are on the screen. The expected number 
of hits within the parts of zones which are on the screen is, how- 
ever, computed from the total number of shots fired (72 in the 
case of Fig. A4). This was done using circular probability paper 
to facilitate the numerical integration to determine the probability 
of hits falling within the partial zones. Multiplying these proba- 
bilities by the total number of shots fired gave the expected num- 
ber of hits in each partial zone. 

Corresponding to each of Figs. A1 to A32, the discrepancy 
between the observed and expected number of hits in each of the 
four zones (or partial zones) was measured by y 1 . P (*.*) in 
Tables A4, A5, A6, and A7 indicates the probability of obtaining, 
in similar samples, as bad or a worse fit between observation 
and expectation than that indicated in the Tables. For Test 1, 
the values of P (y a ) in Tables A4 and A5 are, in general, large 
enough so that the fit of the observed distribution to the theoret- 
ical one is acceptable. Thus, for subsequent calculations, the 

ORO-T-160 81 







1AT10N 



more convenient theoretical distribution can with confidence be 
used in place of the observed distribution. The discrepancy 
between the observed and theoretical distributions in Test 2 are 
on the whole greater than for Test 1. 

Undoubtedly, this arises either from a large bias in the mpi 
for shots fired by some of the riflemen, or from nonhomogeneity 
in the dispersion for all the riflemen. However, as Figs. A34 
and A35 indicate, the radial dispersions, s r , are not very differ- 
ent in the two tests so that subsequent conclusions based on dis- 
persion indicated by the straight lines (or equations) of Figs. A34 
and A35, will not be much in error. 

Remarks on the Homogeneity 
of Results for Individual Riflemen 

Attempts were made to identify each bullet hole according to 
the man firing in the case of those tests in which men fired indi- 
vidually. In many cases, it turned out that holes were obviously 
improperly marked. Because of the small number of shots fired 
by each man, the results of individuals could be compared reli- 
ably only if the location of all shots fired was known. Thus, the 
comparison of individuals is limited to the situation of Figs. A1 
and A9. The test for homogeneity consisted, in the case of Fig. 
Al, in counting the number of shots each individual fired inside 
and the number outside the probable error circle, and testing 
this against the expected number based on the results for all 
riflemen. The following table indicates the results for Fig. Al: 



Man No. 


1 


2 


3 


4 


5 


6 


7 


8 


9 


10 


11 


12 


Total 


No. inside 9, 
p.e. circle 


0 


4 


4 


5 


2 


5 


7 


7 


5 


6 


1 


2 


48 


No. outside a 
p.e. circle 


8 


4 


4 


3 


6 


3 


1 


1 


3 


2 


7 


6 


48 



a The expected number throughout is 4. 



Applying the y s test, P = 0.003, for the hypothesis that there 
is no difference (in the long run) among the several individuals, 
the value of P indicates a likelihood of some difference among 
the individuals, which for subsequent purposes is not serious, 
mainly because some individuals (Nos. 1 and 11) appear worse 
than the average, while others (Nos. 7 and 8) appear better. 
This somewhat compensates, so that the distribution of all 
shots does not deviate seriously from the expected distribution 



82 



ORO-T-160 



N 



(see P (y 1 ) Tables A4, A5, A6, and A7). Similar tests for the 
results in Fig. A 9 are given in the following table: 



Man No. 


1 


2 


3 


4 


5 


6 


7 


Total 


No. inside a 
p.e. circle 


1 


4 


5 


4 


7 


2 


4 


27 


No. outside a 
p.e. circle 


7 


4 


3 


4 


1 


6 


4 


29 



a The expected number throughout is 4. 



Here P (y 2 ) = 0.08, indicating no statistically significant depar- 
ture from homogeneity of results for the seven individuals. 



Remarks on Deviations of mpi from Aiming Point 

In connection with Fig. A36, it is reasonable to expect some 
systematic vertical deviations in mpi with range; because of 
this, tests of the vertical deviation of the mpi from an aiming 
point were not made. However, deviations of the mpi to the 
right or left (x coordinate) from the vertical line through the 
center of the target were tested to determine whether they were 
large enough to be statistically significant. The results are 
shown in Tables A4, A5, A6, and A7 in which P (x) indicates 
the probability of obtaining (in further samples under similar 
circumstances) deviations of the mpi as great or greater than 
those actually observed. It is evident in Tables A4 and A5 that, 
in most cases, the deviations are not statistically significant. 

For Test 2 as shown in Tables A6 and A7 several small values 
of P were obtained. This indicates that many of the deviations 
are statistically significant, particularly since Table A2 and 
Fig. A37 show that all the mpi, in Test 2, deviated to the 
right (x, positive). It should be mentioned, however, that if 
the mpi for some of the individual riflemen deviate significantly 
from the mpi averaged for all, then the deviations of single 
shots from the latter mpi are not statistically independent. 

Taking account of this would increase the values of P (x) in the 
Tables. In any case, the deviations of the mpi (x in Tables A4 
and A5) in Test 1 were not, in general, significant so that 
subsequent calculations will apply reasonably well to conditions 
of Test 1. 

ORO-T-160 83 






10 



-X- 

100 



J- 

300 



400 






200 

RANGE (YD) 



(§) Experts 0 Marksmen 




Fig* A3 6 — Distance of mpi from top of target as function of range; 
combined individual and simultaneous firings of experts and marksmen; 
Tests 1 and 2. 



84 




9C< 



ORO-T-160 






INCHES , INCHES 



mm 



15 
10 
5 
0 

-5 
10 

0 100 200 300 400 

RANGE (YD) 

O Experts firing individually A Marksmen firing individually 

X Experts firing simultaneously O Marksmen firing simultaneously 




15 



10 



5 



0 



”5 



-10 

0 100 200 300 400 

RANGE (YD) 

Fig* A37 — Distance of mpi from vertical line through target center as 
function of range; marksmen and experts firing individually and 
simultaneous ly, Test 1* 




ORO-T-160 



85 






INCHES INCHES 



*^%*ECimnr 




O Experts firing individually 
X Experts firing simultaneously 



A Marksmen firing individually 
□ Marksmen firing simultaneously 




Fig. A38 — Distance of mpi from vertical line through target center as 
function of range; marksmen and experts firing individually and 
simultaneously. Test 2. 



86 » C ORO-T-160 

L’ !■ ’ 

^'■ yuamnn S ra t H - " mPMMtioN 



siLuimii 5TIIIEI 11,1 lUiuiuMMi 



Comparison of Observed and Theoretical 
Probabilities of Hitting Target at Various Ranges 

Figures A39 and A40 compare the observed and theoretical 
probabilities of hitting the target at different ranges under the 
several conditions involved in Tests 1 and 2. The observed 
probabilities are, of course, just the percentage hits on the 
target, from Fig. A1 to A32. The theoretical probabilities, 
shown by the curves of Figs. A3 9 and A40 were computed on 
the basis of the following model: (a) The target was assumed 
to have the shape and dimensions shown in the accompanying 
sketch: 




The location of the assumed mpi for all ranges is shown; 
it is on the vertical center line through the target, (b) The 
standard deviation of radial deviations, for any particular 
range, was assumed to be that given by the lines (or equations) 
in Figs. A34 and A35. 

Tests show that the deviations of some of the "observed 
points" from the curves, in Figs. A39 and A40, are statisti- 
cally significant. These deviations are generally below the 
curve. In Fig. A40, for example, all the crosses in the upper 
figure fall below the curve. Examination of Table A2 indicates 
that the mpi (the x's in the Table) were all to the right of the 
vertical center line through the target; moreover, the small 
values of P (x) in Table A7 indicate that these deviations of the 



ORO-T-160 



87 



*™» S M HEf 



tATSON 



PROBABILITY 




Fig. A39 — Probability of expert riflemen hitting Type E silhouette of range. Ei: firing 
individually; Es: firing simultaneously. 



88 



ORO-T-160 



isq 



S K RET WMfeRTION 



PROBABILITY 






Fig. A40 — Probability of marksmen hitting Type E silhouette target as a function of 
range. Mi: firing individually; Ms: firing simultaneously. 



ORO-T-160 



89 






mpi from the center line were statistically significant. Never- 
theless, the curves give a fair approximation to observed 
results, at least for Test 1. In fact, the differences between 
the theoretical probabilities of hit and those observed in Test 1 
are, in general, comparable with the differences between the 
observed probabilities in Test 1 and those observed in Test 2. 

At the range of 205 yd, all the observed points fall below the 
curves. In Figs. A34 and A35 it may also be seen that the 
observed standard deviations obtained for range 205 yd, appear 
to be consistently high. Observers at the firing range indicated 
that the target appeared to be as far away as that at 265 yd. 

This may have been an illusion due to some bushes close to 
the line of sight. If sufficient data were available to determine 
from a large number of samples the nature of the distribution of 
mpi, this could be used in the determination of theoretical proba- 
bilities. In any case, the theoretical curves and the hypotheses 
on which they were derived provide a convenient and sufficiently 
good basis on which to compare probabilities of hitting targets 
with a single-shot weapon and a hypothetical one which fires 
several shots simultaneously in a pattern. 



Remarks on Results of Firing on Targets 
Appearing Randomly at Either of Two Ranges 

Table A3 indicates the results obtained when the target (type 
E silhouettes) appeared randomly, and for 1 sec. , at either of 
two ranges (110 yd or 265 yd) as described in the introduction. 
Due to the small number of rounds fired and especially to the 
very small number of hits on the target, inspection of Table A3 
indicates that for any particular range the differences between 
the percentage hits on the target are not statistically significant 
for experts firing individually (Ej) compared to experts firing 
simultaneously. For Test 3 the same conclusion obtains for 
marksmen. Thus, from Table A3 the results Ej and E a were 
combined for each of the two ranges; results for and M s 
were similarly combined. When the combined results for 
experts in Test3 at range 110 yd were compared with the results 
of experts firing simultaneously from Tests 1 and 2, at 110 yd, 
the percentage hits on the target were definitely less in Test 3, 
and the difference was found to be statistically significant. Simi- 
larly, the combined results for experts in Test 3 at 265 yd 
indicated a significantly lower percentage hits than that obtained 
from the combined results, in Tests 1 and 2, of experts firing 



90 



ORO-T-160 



simultaneously at range 265 yd. That is, as would be antici- 
pated, the accuracy of expert riflemen for the same range was 
much less under the conditions of Test 3 than under the conditions 
of Tests 1 and 2. For the marksmen, the results from Test 3 
were not statistically different from those of Tests 1 and 2 
at the same ranges. 



APPLICATION 

Theoretical Probability of Hitting 

Type E Silhouette Target With a Salvo Pattern 

In the same way that the results of the present analysis were 
used to compute the curves of Figs. A39 and A40, they may also 
be used to obtain the variation, with range, of the probability 
of hitting the target with a salvo pattern. In Fig. A41, the curves 
M„(l) and E t ( 1 ) are respectively the curves M s of Fig. A40, and 
Ej of Fig. A39. The curves M s (l) and Ej(l) were obtained for the 
target, sketched previously, in the following way: The right half 
of the target can be considered made up of two rectangles: one 5 
in. x 38 in. , and the other 5 in. x 28 in. ; with A as mean, the 
independent probabilities of x and y falling inside each of the rec- 
tangles are readily found from tables of the probability integral 
since the standard deviations of x and y are known for any range; 
for each rectangle the product of the two probabilities gives, of 
course, the probability of both x and y being in the rectangle; 
summing over both rectangles and multiplying by 2 gives the 
probability of hitting the target. 

In Fig. A41, the curves Ej(2) and Mg (2) were computed for 
the five -shot pattern drawn as it would hit a screen at 300 yd 
range. It was assumed that there was no statistical dispersion 
in the position (at the target) of any one of the individual missiles 
relative to the others. It was also assumed that the "spread" of 
the pattern was proportional to range. The dispersion of the 
center missile (the others in the pattern remain fixed relative 
to the center missile) at the target was assumed to be the same 
as that used in computing the curves E { (1) and M s (l), i. e. , that 
derived from the analysis of the aiming errors obtained in the 
tests. For each range a "virtual target" was drawn such that 
if the aimed round of the pattern (i. e. , the central one) fell 
inside the boundary of the virtual target then at least one missile 
hit the target. Except for the fact that the "virtual target" was 
somewhat more complex in shape, the procedure used to obtain 



ORO-T-160 



91 



PROBABILITY 



SECURITY 



INFORMATION* 




92 



Fig. A41 — Probability of hitting E type silhouette target with single 
shot compared with probability of at least one hit with a five-shot 
pattern salvo; curves based on aiming errors. E*: experts firing indi- 
vidually; M s : marksmen firing simultaneously; (1) with single shot; 
(2) at least one hit with five-shot pattern I; (3) at least one hit with 
five-shot pattern II. 





ORO-T-160 



secu ; 



iRMATJpN 



PROBABILITY 



SECURl 






Unclassified 

the probability of obtaining at least one hit was the same as that 
described above for single shots (i. e. , no pattern). 

The curves Ej (3) and M g (3) were similarly computed for 
the same shape of salvo pattern, but for a pattern with half the 
spread (at any given distance) as that used for E t (2) and M a (2). 
From Fig. A41 it is evident that, of the two shot patterns, the 
one with the greater spread has the over -all advantage over 
ranges up to 300 yd. Incidentally, the probability of at least 
one hit, on type E silhouette, indicated by curves E. (2) and 
M s (2), Fig. A41, for ranges up to 225 yd applies also to the 
four -shot pattern resulting from removal of the center shot from 
pattern I. Curves Ej (3) and M a (3) apply also to the four -shot 
pattern resulting from the removal of the central bullet of 
pattern II. 



Probabilities for 1. 2. 3, 4, and 5 Hits 
on Man-Size Target With Five -Shot Pattern Salvo 

The probabilities of 1, 2, 3, 4, and 5 bullets hitting a 
target are given in Tables A8 and A9 for marksmen and for 
experts individually firing a five -shot pattern salvo. The 
target, type E silhouette, is that sketched previously. The 
shot pattern used in the calculations is pattern I as sketched 
in Fig. A41. It should be noted that, in the case of multiple 
hits, the individual hits are not located at random relative to 
each other. This follows from the assumptions stated previously 
to the effect that on arrival at the target the relative positions of 
all missiles in the pattern are fixed, with the dimensions of the 
pattern proportional to range. 

Comparison of Theoretical Probabilities of Hitting 
"Average Target" with Single -Shot and Five-Shot Pattern Salvo 
At the eye of a rifleman, the solid angle subtended by the 
average human target in combat is less than that subtended by 
the type E silhouette. 1 For the approximation to the average 
target a rectangle (for convenience in calculation) 20 in. x 12 in. 
was chosen and designated target A (see Fig. A42). The proba- 
bility of hitting target A as a function of range was computed giving 
the results shown by the curves in Fig. A42. These curves indicate 
that the probability of at least one hit with the five -shot pattern 
salvo is decidedly greater, for the same range, than the probability 
of hitting with a single shot. If the central bullet is removed from 



l ORO-R-5 






ORO-T-160 



93 



PROBABILITY 



SECURI^tKHW^FORMATION 



1 




RANGE (YD) 



CO 

< 

CO 

O 

£L 



Fig* A42 — Probability of hitting “average" target, A, (sketched in 
box) with single shot compared with probability of at least one hit on 
target with five-shot pattern salvos. E j : experts firing individually; 
M $ : marksmen firing simultaneously; (4) with single shot; (5) at least 
one hit on target with five- shot pattern I. 



94 



ORO-T-160 



SECI 



In 



the five -shot pattern the probability of at least one hit on target A 
is unaffected at ranges less than 150 yd. 

Remarks on Significance of Probabilities of Hitting a Target 
with a Single-Shot and with Five-Shot, Four -Shot Pattern Salvos 
Although the probability of at least one hit on the target is, at 
the same range, greater for one five -shot pattern salvo than for 
a single shot, it is less then the probability of at least one hit on 
the target for five separately aimed single shots. Consider, for 
example, the comparison at 200 yd range for the upper curves in 
Fig. A42. For the five -shot pattern, curve Ej(5) indicates at 
200 yd a probability of about 0.74 for at least one hit. For one 
single shot, curve Eg (4) indicates about 0.32 for the hit probability. 
The probability of at least one hit in five single-shot trials is then: 

(1 - 0.68*) = 0.85 which is somewhat greater than the probability 
of 0.74 for at least one hit for the five-shot pattern. 

Consider also the case for range 150 yd for target A. The curve 
Eg (4) of Fig. A42 shows for range 150 yd a probability of 0.49 for 
hitting target A. Curve E. (5) indicates 0.90 for the probability of 
at least one hit using the five-shot pattern. As indicated in the 
preceding section, the probability of at least one hit for the four- 
shot pattern (central one of the five-shot pattern removed) is, for 
ranges less than 150 yd, the same as for the five-shot pattern. 

Thus, the probability of at least one hit, in this case, from five 
single shots is (1 - 0.51 s ) = 0.97 which is slightly greater than that 
for at least one hit from a single five -shot pattern salvo. However, 
if we use a four-shot pattern we find (1 - 0.5 1 4 ) = 0.93 for the proba- 
bility of at least one hit from four single shots compared to 0.90 
for the probability of at least one hit from the four -shot pattern. 
Thus, for targets which may remain in the rifleman's view only 
long enough for him to aim once, the advantages of the five -shot 
pattern salvo are evident. 

Effect of Weapon Dispersion on Probability of Hitting Target 

In order to determine the effect of weapon dispersion (the 
dispersion at the target when the rifle is rigidly fixed) on the 
probability of hitting the target, it is necessary to determine the 
standard deviation due only to aiming. From the firing test data 
the total standard deviation, a t , at the target was found to be 
proportional to the range, that is 

a T ~ cr in. (l) 

with r the range in units of 100 yd. 

• » i * Jjf 

ORO-T-160 95 



SEC I 



»<B« 



Let tr w represent the standard deviation due to weapon dispersion 
(i. e. , standard deviation of shot distances from mpi). Now the 
standard deviation at the target, due only to weapon dispersion, 
will also be proportional to the range r, then: 



Also the standard deviation, <7 A , due to aiming errors only (i.e.,no 
weapon -ammunition dispersion) will be proportional to the range, thus: 



Since deviations from the mpi due to aiming errors and to weapon- 
ammunition errors are independent, than at a particular range: 



Tests on the M-l rifle indicate that a= 2.3 in.; that is, the 
standard deviation of shot distances from the mpi, for a rigidly 
held rifle, is 2.3 in. at 100 yd. (i.e., r = 1), including dispersion 
due to ammunition. This determines A in Equation 5 when c is 
known. From Table A5 the value of c is 9.0 in. for marksmen 
firing individually. For this case, and using oc= 2.3 in., Equation 
5 determines A = 76. Thus for other weapon dispersions, k x 2.3, 
the variance^ 2 of the combined errors due to weapon- ammunition 
and aiming is given by: 



Consider target A which, as previously described, is a rectangle 
20 in. x 12 in. The probability of hitting this target (mpi at center) 
is, to a degree of approximation sufficient for present purposes, the 
probability of hitting a circular target with the same area. Thus, 
for convenience in estimating the effect of weapon dispersion on 
probability of hitting, consider the circular target with radius a 
such that it s? = 240 in. 2 , (12 in. x 20 in.) from which a 2 = 76.5 
(a = 8.75 in.). For the mpi at the center of the circle, the probability, 
P m , of missing the target (i.e. , of shots falling outside the circle 
of radius a) is: 



for marksmen firing individually. The three lines designated 



cr w = Otr in. 



( 2 ) 



= At in. 



(3) 



o; 



T 



2 



a K + < 



2 



(4) 



or for any range r: 



A 2 r* +0tk 2 r 2 



(5) 



'r 



2 



= r 2 (76 + 5k 2 ) 



( 6 ) 



p. 



m 




e 



-76.5/r*(76 + 5k 2 ) ^ 



in Fig. A43 are the curves of Equation (7) for each of three values 



96 




ORO-T-160 



5EO 



M&MfwaiftyioN 






3 : 



y* 




o 

QC 

< 

O 

z 

I- 



LL 

O 



_J 

cfi 

< 

£0 

O 

Q£ 

CL 



Fig. A43 — Probability of hitting a circular target of area = 240 sq in. (radius = 8.75 in.) 
as a function of range for several weapon-ammunition errors. Plotted for marksmen 
firing individually, Mj; and experts firing individually, Ej. k is a selected multiple of 
the standard deviation of the strike from the mpi, as caused by weapon and ammunition 
alone. Thus k - 1 represents actual performance with issue rifle and ammunition, k =0 
shows performance with perfect weapons and ammunition, and k = 2 indicates 
performance with weapons and ammunitions giving double the actual standard deviation. 



of k. From these curves (Mj) it will be seen that the probability 
of hitting for K = 0 (i.e., no weapon -ammunition dispersion) is 
only slightly less than k = 1 (i.e., for the actual dispersion of 
the M-l rifle and ammunition). Also, the curves for k = 2 
indicate probabilities of hitting which are still not significantly 
less than those for a dispersionless rifle and ammunition (k = 0). 
The four lower curves (Ej) in Fig. A43 apply to experts firing 
individually, for which the equation is: 

P = e " aV V = e -76.5/r»(42.5+5k 2 ) 
m ' * 

Equation 8 is obtained in the same manner as Equation 7 starting 
with the value of 6.9 in. for c, obtained from Table A4 for experts 
firing individually. 



ORO-T-160 






ORO-T-160 



00 



TABLE A1 

RIFLE RANGE TEST 1 



Men 


Range, 




y* 


Std. 


Deviation, in. 


No. Men 


Rounds 


Total 


No* Rounds 


% on 


yd 


/ in* 


in. 


X 


y 


r 


Firing 


per man 


Rounds 


Target 


Screen 


Target 


E i a 


110 


- 0.9 


13*5 


4.1 


5.2 


6.4 


12 


8 


96 


88 


96 


0.917 




205 


- 0.5 


16.0 


13.5 


15.0 


20.2 


10 


8 


80 


36 


69 


0.450 




265 


~ 3.0 


19.5 


13*0 


13*0 


18.4 


9 


8 


72 


34 


62 


0.472 




310 


+ 6.0 


7.0 


12.6 


17.8 


21.8 


9 


8 


72 


28 


47 


0.389 


E s b 


110 


+ 1.2 


8.7 


4.1 


11.2 


11.9 


8 


4 


32 


20 


24 


0.625 




205 


- 2.8 


15.6 


11.0 


12.8 


16*9 


8 


4 


32 


12 


26 


0.375 




265 


- 5.9 


11.0 


8*4 


17.2 


19.1 


8 


4 


32 


11 


21 


0.344 




310 


- 8.2 


10.0 


15*0 


18.3 


23.7 


8 


4 


32 


9 


19 


0,281 


Mi e 


110 


- 1.7 


16.4 


8.7 


6.4 


10.8 


7 


8 


56 


39 


56 


0*696 


205 


- 2*0 


15.2 


13*0 


14.5 


19.5 


9 


8 


72 


19 


58 


0.264 




265 


+ 4.8 


18.3 


17*2 


14.0 


22*2 


9 


8 


72 


25 


65 


0.347 




310 


- 1.0 


14.8 


24.0 


12.2 


26.9 


10 


8 


80 


24 


61 


0*300 


M s d 


110 


- 1.8 


14.2 


14.2 


9.0 


16.8 


8 


4 


32 


12 


30 


0.375 


205 


+ 10.5 


11.8 


23.0 


20.2 


30.6 


8 


4 


32 


4 


19 


0*125 




265 


- 2.5 


31.5 


25.1 


13,9 


28.7 


3 


4 


32 


6 


32 


0.188 




310 


+ 1.0 


17.2 


36.0 


15.8 


39.3 


8 


4 


32 


4 


25 


0.125 



- Expert Riflemen Individually Firing at Target. - Marksmen Individually Firing at Target. 

E g - Expert Riflemen Simultaneously Firing at Target. - Marksmen Simultaneously Firing at Target. 



ORO-T-160 



TABLE A2 

RIFLE RANGE TEST 2 



Men 


Range, 

yd 


x, 

in. 


y * 

in. 


Std. 


Deviation, in. 


No. Men 
Firing 


Rounds 
per man 


Total 

Rounds 


No. Rounds 


% on 
Target 


X 


y 


r 


Target 


Screen 


E. a 


110 


+ 


0.6 


15.4 


5.2 


6.9 


8.6 


12 


8 


96 


81 


91 


0.844 


1 


205 


+ 


5.7 


18.0 


14.8 


14.5 


20.7 


8 


8 


64 


22 


45 


0.344 




265 


+ 


3.4 


14.1 


9.4 


13.1 


16.1 


8 


8 


64 


30 


56 


0.469 




310 


+ 


12.5 


23.5 


13.5 


13.1 


18.8 


10 


8 


80 


35 


77 


0.438 


E s b 


110 


+ 


0.8 


20.5 


2.8 


9.3 


9.7 


8 


4 


32 


28 


28 


0.875 




205 


+ 


3.9 


23.0 


17.1 


14.3 


22.3 


16 


4 


64 


19 


58 


0.297 




265 


+ 


1.7 


17.0 


10.1 


12.8 


16.3 


8 


4 


32 


13 


28 


0.406 




310 


+ 


2.5 


13.9 


21.5 


14.1 


25.7 


8 


4 


32 


8 


25 


0.250 


Mj c 


110 


+ 


5.8 


23.4 


6.8 


7.1 


9.8 


8 


8 


64 


34 


64 


0.531 


205 


+ 


14.1 


26.6 


23.1 


17.9 


29.2 


9 


8 


72 


12 


59 


0.167 




265 


+ 


15.2 


20.2 


19.5 


11.4 


22.6 


12 


8 


96 


19 


88 


0.198 




310 


+ 


19.1 


17.0 


24.1 


23.3 


33.5 


10 


S 


80 


12 


61 


0.150 


M d 


no 


+. 


2.2 


26.7 


10.5 


8.1 


13.3 


8 


4 


32 


18 


29 


0.562 


s 


205 


+ 


12.1 


24.5 


18.5 


18.0 


25.8 


16 


4 


65 e 


10 


49 


0.154 




265 


+ 


9.2 


14.4 


12.7 


20.1 


23.8 


8 


4 


32 


8 


24 


0.250 




310 


+ 


10.8 


21.3 


17.2 


23.7 


29.3 


8 


4 


32 


2 


26 


0.062 



®E. - Expert Riflemen Individually Firing at Target, - Marksmen Simultaneously Firing at Target. 

b E 1 g - Expert Riflemen Simultaneously Firing at Target. e Qne Man Fired Five Rounc *s. 

C M. - Marksmen Individually Firing at Target. 






100 ORO-T-160 



TABLE AS 



RIFLE RANGE TEST 3 

FIRING AT TARGETS NO* 1 AND NO. 3 ALTERNATELY ON RANDOM SCHEDULE 



Men 


Range, 

yd 


x, 

in. 


y * 

in. 


Std. 


Deviation, in. 


No. Men 
Firing 


Rounds 
per man 


Total 

Rounds 


Number Rounds 


% on 
Target 


Not 

Expend. 


On 

Target 


On 

Screen 


X 


y 


r 


E. a 


110 


- 4.4 


16*8 


20.2 


21.4 


29.4 


4 


4 


15 


1 


4 


11 


0.267 




265 


0.0 


23.0 


20.0 


15.9 


25.6 


4 


4 


16 


0 


1 


13 


0.062 


E a b 


110 


+ 4.0 


7.9 


18.0 


11.3 


21.3 


4 


4 


11 


5 


2 


7 


0.182 




265 


+ 4*0 


* 8.0 


21.0 


24.8 


32.5 


4 


4 


16 


0 


0 


6 


0.000 


Mi c 


110 


- 1.8 


16.7 


13.4 


8.7 


16.0 


4 


4 


14 


2 


7 


14 


0.500 




265 


- 1.4 


6.9 


41.1 


23.5 


47.3 


4 


4 


15 


1 


1 


8 


0.067 


M s d 


110 


- 10.8 


13.0 


11.6 


15.4 


19.3 


4 


4 


13 


3 


4 


10 


0,308 




265 


- 2.7 


- 7.0 


15.4 


19.5 


24.8 


4 


4 


16 


0 


3 


6 


0.188 



- Expert Riflemen Individually Firing at Target. 

E g - Expert Riflemen Simultaneously Firing at Target, 



- Marksmen Individually Firing at Target, 
a M g - Marksmen Simultaneously Firing at Target. 



TABLE A4 



.ON 



COMPARISON OF OBSERVED NUMBER OF SHOTS INSIDE ZONES 
BOUNDED BY CIRCLES OF RADII r t , AND r a , IN., WITH 
NUMBER EXPECTED FROM BIVARIATE DISTRIBUTION WITH RADIAL 
STANDARD DEVIATION a x \ AT FOUR RANGES, R, IN YD: TEST 1 



(A) Experts Individually o t = 6.9 R/100 {a t in in.) 

(<7 = a = 4.87 R/100, in.) 
x y 



R(yd) 110 


205 


265 


310 


ff r 7.6 


14.1 


18.3 




21.4 


Zone 


No. in Zone 


Zone 


No. in Zone 


Zone 


No. in Zone 


Zone 


No. in Zone 


r r 

1 2 


Obsd Exptd 


r r 

1 2 


Obsd Exptd 


r r 

1 2 


Obsd Exptd 


r r 

t 2 


Obsd Exptd 


0 4.1 

4.1 6.3 

6.3 9.0 

9.0 <» 


25 24 

28 24 

23 24 

20 24 


0 7.6 

7.6 11.7 
11.7 16.6 
16.6 •» 


15 20 

14 20 

18 20 

33 20 


0 9.8 

9.8 15.2 
15.2 21.6 

21.6 oc 


23 18 

19 18 

12 18 

18 18 


0 11.5 

11.5 17.8 
17.8 25.2 
05.2 B) b 


20 d 16 d 

12 d 12 d 

7* 1 ll d 


On Screen 
Off Screen 
Total 

P(x 2 ) 

P(x) 


96 

0 

96 96 

0.75 
0.10 


69 

U a 

80 80 
0.01 
0.66 


62 

10 a 

72 72 

0.25 
0.05 


47 50 

25° 22° 

72 72 

0.5 
10~ 4 


(B) Exp 


erts Simultaneously a T = 7.8 R/100 (<r r in in.) 
{a = a =* 5.51 R/100, in.) 

x y 


R(yd) 110 


205 


265 


310 


a T 8.6 


16.0 


20.7 


24.2 


Zone 


No* in Zone 


Zone 


No. in Zone 


Zone 


No. in Zone 


Zone 


No. in Zone 


r r 

l .2 


Obsd Exptd 


r r 

1 2 


Obsd Exptd 


r r 

1 2 


Ob$d Exptd 


r r 

1 2 


Obsd Exptd 


0 4.6 
4.6 7.1 
7.1 10.1 
10.1 


9 8 

5 8 

4 8 

14 8 


0 8.6 

8.6 13.3 
13.3 18.9 
18.9 L ~ 


8 8 

7 8 

5 8 

12 8 


0 11.1 

11.1 17.2 

17.2 24.4 
@4.4 B) b 


7 8 

5 d 5 d 

2 d 5 d 


0 13.0 

13.0 20.1 

20.1 28.5 
@8,5 B) b 


3 d 6 d 

4 d 5 d 


On Screen 24 
Off Screen 8 a 
Total 32 32 

P(X 2 > 0.05 

P(x) 0.27 


26 

6 a 

32 32 

0.75 
0.17 


21 24 

11° 7° 

32 32 

0.4 
0.02 


19 24 

13 c 8 C 

32 32 

0.25 
0.01 



a Off screen in outermost zone. *|Off screen; zone unknown. 

^Outside but on screen. “Within zone and on screen. 

p ( X 2 ) probability of obtaining as bad or worse fit between observed and expected numbers. 
P ( X ) probability of obtaining mpi as far or farther from vertical center line of target. 




ORO-T-160 



101 



TABLE A5 

COMPARISON OF OBSERVED NUMBER OF SHOTS INSIDE ZONES 
BOUNDED BY CIRCLES OF RADII r„ AND r 2 , IN., WITH 
NUMBER EXPECTED FROM BIVARIATE DISTRIBUTION WITH RADIAL 
STANDARD DEVIATION a f \ AT FOUR RANGES, R, IN YD: TEST 1 



(A) Marksmen Individually a r = 9.0 R/100 (a in in.) 

(a = a = 6.36 R/100, in.) 

x y 



R(yd) 110 


205 


265 


310 


a T 9.9 


18.4 


23.9 


27.9 


Zone 


No. in Zone 


Zone 


No. in Zone 


Zone 


No. in Zone 


Zone 


No. in Zone 




Obsd Exptd 


*1 r 2 


Obsd Exptd 


r l r 2 


Obsd Exptd 


r i r 2 


Obsd Exptd 


0 5.3 

5.3 8.2 

8.2 11.7 
11.7 « 


18 14 

10 14 

11 14 

17 14 


0 9.9 

9.9 15.4 
15.4 21.8 
(21.8 B) b 


11 18 

10, 18 h 

13 d 15 d 

24 d 13 d 


0 12.8 

12.8 19.9 

19.9 28.0 
(28.0 B) b 


«, 18 h 

18 d 18 d 

20 d 14 d 

12 d 12 d 


0 15.0 

15.0 23.2 
23.2 32.9 
(32.9 B) b 


22 20 

14 d 16 d 

15 d 16 d 

10 d 12 d 


On Screen 56 
Off Screen 0 
Total 56 56 

P(X*) 0.25 

P(x) 0.07 


58 64 

14 a 8 a 

72 72 

10 
0.07 


65 62 

7 a 10 a 

72 72 

0.3 
0.02 


61 64 

19 a 16 a 

80 80 

0.9 
0.7 



(B) Marksmen Simultaneously = 13.0 R/100 (a r in in.) 

{a = a — 9.2 R/100, in.) 

x y 



-R(yd) 110 


205 


265 


310 


or 14.3 

r 


26.6 


34.5 


40.3 


Zone 


No. in Zone 


Zone 


No. in Zone 


Zone 


No. in Zone 


Zone 


No. in Zone 


r i r a 


Obsd Exptd 


r i r 2 


Obsd Exptd 




Obsd Exptd 


r i *2 


Obsd Exptd 


0 7.7 

7.7 11.9 
11.9 16.9 
(16.9 B) b 


5 8- 

7 8 

9 d 8 d 

9 d 6 d 


0 14.3 

14.3 22.2 
22.2 31.4 
(31.4 B) b 


4 d 8 d 

2 d 6 d 

8 d 5 d 

5 d 4 d 


0 18.4 

18.4 28.7 
28.7 40.6 
(40.6 B) b 


11 8 

13 d 8 d 

3 d 5 d 

5 d 3 d 


0 21.6 

21.6 33.6 

33.6 47.5 
(47.5 B) b 


ll d 8 d 

A ftd 

Id Jd 

S d 2 d 


On Screen 30 30 

Off Screen 2 a 2 a 

Total 32 

P( X ») 0.5 

P(x) 0.3 


19 23 

13 a 9 a 

32 32 

0.1 

2 x 10 


32 24 

0 a S a 

32 32 

0.01 
0.6 


25 20 

7 a 12 a 

32 32 

0.2 
0.8 



®Off screen, zone unknown. 

^Outside r x but on screen. 
a Within zone and on screen. 

P( X 2 ) probability of obtaining as bad or worse fit between observed and expected numbers. 
P ( x ) probability of obtaining mpi as far or farther from vertical center line of target. 



102 



ORO-T-160 



f ; 



TABLE A6 

COMPARISON OF OBSERVED NUMBER OF SHOTS INSIDE ZONES 
BOUNDED BY CIRCLES OF RADII r„ AND r 4 , IN., WITH 
NUMBER EXPECTED FROM BIVARIATE DISTRIBUTION WITH RADIAL 
STANDARD DEVIATION o f AT FOUR RANGES, R, IN YD: TEST 2 



(A) Experts Individually o T - 6.9 R/100 (er f in in.) 

{a = o = 4.87 R/100, in.) 
x y 



R(yd) 110 


205 


265 


310 


o, 7.6 


14.1 


18.3 


21.4 


Zone 


No. in Zone 


Zone 


No. in Zone 


Zone 


No. in Zone 


Zone 


No. in Zone 




Obsd Exptd 


p i r* 


Obsd Exptd 


r i 


Obsd Exptd 


r i P 2 


Obsd Exptd 


0 4.1 

4.1 6.3 

6.3 9.0 

9.0 °° 


15 24 

23 24 

22 24 

36 24 


0 7.6 

7.6 11.7 
11.7 16.6 
16.6 


9 16 

8 16 

9 16 

38 16 


0 9.8 

9.8 15.2 
15.2 21.6 
21.6 B) c 


20 16 

14 j 16 

14“ 13“ 

8 d ll d 


0 11.5 

11.5 17.8 
17.8 25.2 
25.2 B) c 


21 20 

31 20 


On Screen 9 1 
Off Screen 5 a 
Total 96 96 

P(x*) 0.02 

P(x) 0.25 


45 

19 a 

64 64 

<0.001 
3x10"* 


56 56, 

8 b 8 b 
64 64 

0.71 
0.04 


77 76 

3 b 4 b 

80 80 

0,02 
2 x 10” 9 




(B) Experts Simultaneously & r = 7.8 R/100 (a t in in.) 

( ff = = g,51 R/100, in.) 

* y 



R(yd) 


110 




205 


265 


310 


°r 


8.6 




16.0 


20.7 


24.2 


Zone 


No. in 


Zone 


Zone 


No. in 


Zone 


Zone 


No. in 


Zone 


Zone 


No. in 


Zone 


Ti T 2 


Obsd 


Exptd 


r i r 2 


Obsd 


Exptd 


r i r 2 


Obsd 


Exptd 


P 1 p 2 


Obsd 


Exptd 


0 4.6 


6 


8 


0 8.6 


6 


16 


0 14.1 


10 


8 


0 13.0 


8, 


8, 


4.6 7.1 


8 


8 


8.6 13.3 


10 


16 


11.1 17.2 


9, 


8, 


13.0 20.1 


2 d 


7 d 


7.1 10.1 


11 


8 


13.3 18.9 


15 


16 


17.2 24.2 


sj 




20.1 28.5 


7? 


ej 


10.1 oo 


7 


8 


18.9 oq 


33 


16 


24.4 B) c 


l d 


6 d 


28.5 B) c 


8 d 


5 d 


On Screen 


28 






58 






29 


29, 




25 


26 


Off Screen 


4 a 






6 a 






4 b 


3 b 




7 b 


6 b 


Total 


32 


32 




64 


64 




32 


32 




32 


32 


PCx 1 ) 


0.63 






<0.001 






0.26 






0.23 




P(x) 


0.49 






0,01 






0.52 






0.42 





f'Off screen in outermost zone. 
D Off screen, zone unknown. 

P( x 1 ) probability of obtaining 
P ( x ) probability of obtaining 



^Outside r x but on screen. 
a Within zone and on screen. 

as bad or worse fit between observed and expected numbers, 
mpi as far or farther from vertical center line of target. 



ORO-T-160 





103 



si 



DECLASSIFIED 



TABLE A7 

I 

COMPARISON OF OBSERVED NUMBER OF SHOTS INSIDE ZONES 
BOUNDED BY CIRCLES OF RADII r„ AND r a , IN., WITH 
NUMBER EXPECTED FROM BIVARIATE DISTRIBUTION WITH RADIAL 
STANDARD DEVIATION a t AT FOUR RANGES, R, IN YD: TEST 2 



(A) Marksmen Individually a t = 9.0 R/100 (a t in in.) 

(<7 = a = 6.36 R/100, in.) 

x y 



R(yd) 110 


205 


265 


310 


a r 9.9 


18.4 


23.9 


27.9 


Zone 


No. in Zone 


Zone 


No. in Zone 


Zone 


No. in Zone 


Zone 


No. in Zone 


i 1 r 2 


Obsd Exptd 


r 2 


Obsd Exptd 


r i *2 


Obsd Exptd 


r i r a 


Obsd Exptd 


0 5.3 

5.3 8.2 

8.2 11.7 
11.7 ~ 


13 16 

21 16 

16 16 

14 16 


0 9.9 

9.9 15.4 
15.4 21.8 
21.8 ~ 


9 18 

9 18 

12 18 

42 18 


0 12.8 

12.8 19.9 

19.9 28.1 

28,1 B)° 


32 24 

20 24 h 

27“ 20“ 

9 d 17“ 


0 15.0 

15.0 23.2 
23.2 32.9 
32.9 B) c 


13, 20 

13 d 18 d 

17 d 14 d 

18 d 13 d 


On Screen 64 

Off Screen 0 

Total 64 64 

PCX 1 ) 0-50 _ 

P(x) <2 xl0“* 


59 

13 a 

72 72 

<0.001 
<2xl0* 9 


88 85 

8 b ll b 

96 96 

0.04 

<2 xlO -9 


61 h 65 

19 b 15 b 

80 80 
0.12 

<2x10“^ 



(B) Marksmen Simultaneously oj. = 13.0 R/100 (ff r in in.) 

(a = cr = 9.2 R/100, in.) 
x y 



R(yd) 110 


205 


265 


310 


o r 14.3 


26.6 


34.5 


40.3 


Zone 


No. in Zone 


Zone 


No. in Zone 


Zone 


No. in Zone 


Zone 


No. in Zone 


*2 


Obsd Exptd 


*1 *2 


Obsd Exptd 


*1 *2 


Obsd Exptd 


r 2 


Obsd Exptd 


0 7.7 

7.7 11.9 

11.9 16.9 

16.9 .» 


13 8 

9 8 

3 8 

7 8 


0 14.3 

14.3 22.2 
22.2 31.4 

31.4 B)° 


16 16 

10 , 16 d 

13 d 15 d 

10 d 12 d 


0 18.5 

18.5 28.7 
28.7 40.6 

40.6 B) c 


13 8 

8 d 6 d 

3 d 5 d 

0 d 5 d 


0 21.6 

21.6 33.6 

33.6 47.5 
47.5 B) c 


13 8 

8 d 6 d 

8 H 5 d 

2 d 5 d 


On Screen 29 
Off Screen 3 a 
Total 32 32 

p(x 2 > 0.09 

P(x) 0.23 


49 l 59 

16 b 6 b 
65 65 

<0.001 
<2 xlO” 9 


24 h 24 

8 b 8 b 
32 32 

0.05 
0.04 


26 24 h 

6 b 8 b 
32 32 

0.15 
0.03 



^Off screen in outermost zone. ^Outside r 1T but on screen. 

b Off screen, zone unknown. Within zone and on screen. 

P ( ) probability of obtaining as bad or worse fit between observed and expected numbers. 

P ( x ) probability of obtaining mpi as far or farther from vertical center line of target. 



104 



DECLASSIFIED 



ORO-T-160 



INFORMATION 




TABLE A 8 



PROBABILITIES, FOR EXPERTS FIRING INDIVIDUALLY, 
OF OBTAINING EXACTLY 1, 2, 3, 4, AND 5 HITS 
ON TYPE E SILHOUETTE WITH FIVE-SHOT PATTERN 
SALVO FOR INDICATED TARGET RANGES 



Range, yd 


Exact No. of Hits 


At least 
1 hit 


1 


2 


3 


4 


5 


100 


0.040 


0.002 


0.049 


0.420 


0.489 


1.000 


150 


0.174 


0.041 


0.269 


0.506 


0.000 


0.990 


200 


0.325 


0.145 


0.398 


0.091 


0.000 


0.959 


250 


0.423 


0.353 


0.125 


0.000 


0.000 


0.901 


300 


0.546 


0.280 


0.000 


0.000 


0.000 


0.826 


350 


0.524 


0.165 


0.000 


0.000 


0.000 


0.689 


400 


0.499 


0.087 


0.000 


0.000 


0.000 


0.586 



TABLE A9 

PROBABILITIES, FOR MARKSMEN FIRING INDIVIDUALLY, 
OF OBTAINING EXACTLY 1, 2, 3, 4, AND 5 HITS 
ON TYPE E SILHOUETTE WITH FIVE -SHOT PATTERN 
SALVO FOR INDICATED TARGET RANGES 



Range, yd 


Exact No. of Hits 


At least 
1 hit 


1 


2 


3 


4 


5 


100 


0.111 


0.011 


0.093 


0.415 


0.360 


0.990 


150 


0.271 


0.066 


0.250 


0.350 


0.000 


0.937 


200 


0.388 


0.122 


0.284 


0.058 


0.000 


0.852 


250 


0.434 


0.240 


0.085 


0.000 


0.000 


0.759 


300 


0.482 


0.186 


0.000 


0.000 


0.000 


0.668 


350 


0.436 


0.108 


0.000 


0.000 


0.000 


0.544 


400 


0.398 


0.057 


0.000 


0,000 


0.000 


0.455 





; U < 



^ j/ ■ . ft* V* 

^ *i £ £i 

THE JOHNS HOPKINS UNIVERSITY 
OPERATIONS RESEARCH OFFICE 
6JblO Connecticut Avenue 
Chevy Chase, Maryland 



a aa'^gas 





18 November 1952 



SUBJECT: Distribution of Project BALANCE Technical Memorandum, QR0-T-160, 

"Operational Requirements for an Infantry Hand Weapon." 



TO: The Deputy Assistant Chief of Staff, G-3, 

for Research, Requirements and Special Weapons 
Department of the Army 
Room 3E37U, The Pentagon 
Washington 25, D. C. 



1. References: 

a. Memorandum, Office of the Assistant Chief of Staff, G-3, 
Operations, f?.le G-3 Oli.0 ORO, dated 22 October 1952, subject: Department 
of the Army Operations Research Office Publication." 

b. Letter, Office of the Assistant Chief of Staff, G-3, RR&SW, 

dated 8 August 1952, subject: "Distribution List for Project BALANCE." 

2. a. Pursuant to paragraph 2, a. Inclosure No. 1, reference a, 
advance copies of 0R0-T-160, "Operational Requirements for an Infantry 
Hand Weapon," by Norman Hitchman, Scott Forbush, and George Blakemore, 

Jr., are transmitted herewith. 

b. It is requested that authority be given for the distribution 
of this document according to the basic Operations Research Office distri- 
bution list, as supplemented by the Project BALANCE list of reference b, 
and to include all the optional addressees on the latter list. 

3. The findings and suggestions presented in this technical memo- 
randum reflect, on the one hand, facts already experimentally determined; 
and, on the other, certain emergent principles relative to the operational 
effectiveness of the general issue rifle. Many of these principles re- 
quire further experimentation in order conclusively to fix details of 
their application. Restatement, as below, of the basic conclusions and 
recommendations, to include both certain additional information as yielded 
to the date of this letter by a continuing study, and also comment as to 
further investigation indicated, may make clearer the extent of present 
knowledge. 




SI 



NWCgtitATtON 



Conclusions:- 



Proven 



Proven 



Proven 



Concluded from analysis; 
suggested as a desirable 
operational principle; 
needs experimental veri- 
fication. 



a ,n 



f « * y, i 



i C ^ 



s^ujoi i i %j 



a. Weapon employment and battlefield 
visibility data, show the limiting 
effect upon ranges of engagement 

for the rifle of both combat practice 
and terrain interruptions to the line 
of sight* It is clearly established 
that the relatively short ranges pre- 
ponderate: "aimed 11 rifle fire is 

delivered at ranges less than 300 
yards about three-quarters of the 
time* There is only a very limited 
need for the capability for such fire 
at greater ranges. Although a distri- 
bution of effect which does not exclude 
all capabilities at those greater 
ranges is required, the weapon should 
be designed to maximize hit probability 
at the more common ranges. (The infre- 
quent exceptions include the sniping 
fire of specially trained and equipped 
riflemen. —Also, it should be noted 
that bearing upon the desirability of 
adopting a single round for all small 
arms is the need for machine-gun fire 
with suitable trajectory and adequate 
wounding power out to 1800-2000 yards.) 

b. In the man-rifle combination, aiming 
errors are generally large— far in ex- 
cess of purely ballistic dispersion. 
Thus, if at any extra cost, the general 
purpose weapon need not be designed to 
provide the current high degree of 
precision. 

c. The hill automatic feature, in rifles of 
the usual design, and in the current US 
experimental models, does not increase 
the expectation of hitting separated 
man-targets. 

d. A controlled dispersion feature, as in- 
corporated in a "salvo" automatic of the 
type proposed, may largely compensate 
for the large aiming errors which 
typically accompany each trigger pull. 



Unclassified 



S! 



SECUl 



'RMATiON 




Proven, i 

at Princeton University, the 
Army Chemical Center, Aber- 
deen Proving Ground, and else- 
where. Tests of bullets, as 
contrasted with spherical 
pellets, have not been ex- 
tended beyond the range of 
calibers .30-. 21. Additional 
experimentation, through a 
range extended downward, is 
required to determine the best 
in. i.3 it ary caliber, from 'the 
standpoint of ’‘wounding power” 
and other considerations. 



At the cost of a small loss in armor 
penetrating ability at some ranges (a 
characteristic of doubtful military 
value in the rifle), a weapon of a 
caliber smaller than .30, providing 
a correspondingly higher velocity, 
offers generally superior “wounding 
power" at the ranges of interest 
(and somewhat beyond); improved ex- 
terior ballistics; lighter ammunition; 
a slightly lighter rifle i and seme 
reduction in recoil. The small cali- 
ber appears especially valuable in 
connection with a "salvo" automatic 
type of shoulder weapon which projects 
four- or five-round dispersion patterns. 
Caliber and other ammunition charac- 
teristics within the following ranges 
appear to offer promise of substantial 
all-round improvement: 

(1) Caliber: .276 (7mm) - .180 (U.57mm). 

(2) Wt. ball: lj.0-60 gr (168 gr for cal- 

iber .30, M2 AP). 

(3) Wt. charge: U0-h5 gr ($3 gr for 

caliber *30, M2 AP). 



(li) Wt. complete round: 250-300 gr (1(16 
gr for caliber .30, M2 
AP). 

(5) Muzzle velocity: 3700-1:800 ft per 

sec (2770 ft per sec 
for caliber .30, M2 
AP). 

(6) Muzzle energy: 1800-2200 ft-lb 

(2800 ft-lb for cali- 
ber .30, M2 AP). 



Proven, as to lethality f. 

of agent; feasibility of 
incorporation in the round 
is estimated from preliminary 
study and expert opinion; 
relative importance of disad- 
vantages has not been weighed. 




/ /"x* 



sccu 



Toxic agents could greatly increase the 
lethality of bullet hits; and the in- 
corporation of such agents in mass pro- 
duced small aims ammunition is judged 
feasible. Disadvantages such as an un- 
avoidable small time delay in producing 
the lethal effect, and the ease with 
which the enemy could retaliate in 
kind, as well as the relative desir- 
ability of killing as contrasted with 



RMATION 



SE< 



INFORMATION 




wounding, would require analysis if 
a policy decision sanctioning the use 
of such agents were made. 



Recommendations 



Experiment and test for g. 

determining details of 
design, for verifying 
engineering and pro- 
duction feasibility, 
and for establishing 
jj t acceptability, 

&:?z- necessary « 



0R0 recommends the manufacture and test 
of experimental weapons and ammunition 
in sufficient quantity, and of a suf- 
ficient range in design type, to permit 
conclusive and specific determinations 
with respect tos 

(1) Verification of the operational 
value of a pattern dispersion feature 
(calculated to maximize hitting at the 
ranges of concern) in a ’’salvo,” or 
controlled burst cyclic, automatic* 

(2) Selection of the best smaller 
caliber for such a weapon, upon the 
basis of all functionally associated 
characteristics . 

(3) The feasibility of designs which 
afford the desired characteristics, 
with sufficient reliability in pro- 
jecting the chosen dispersion pattern, 
with controlled length of burst if a 
cyclic weapon, and without objection- 
able cumulative recoil effects. 



U. Further experimentation and test of the sort indicated need not 
be very expensive nor time consuming. Certain positive information of 
real importance and immediate application, long lacking in the procedures 
by which military characteristics are set, and rifles and ammunition are 
designed, could be provided without undue effort. Caliber, for example, 
has been the subject of such prolonged controversy, is now still so dis- 
puted within the NATO (despite a small, measure of agreement on the standard- 
ization of ammunition wrung from the Standing Group), and has. in the past 
been so often fixed by arbitrary ruling, that it is high time all the 
relevant facts as to caliber and ballistics were established upon a firm 
experimental basis. Again, a positive criterion of ’’wounding power” should 
be found and related to tactical employment of the rifle. Finally, both the 
design and performance of a shoulder weapon incorporating the novel controlled 
dispersion feature should be put to actual test* 



1 Incl 

ORO-T-160 (copies 2 to 10) 

Copies (less incl) fhmished 
Director, ORO 
Editor, 0R0 
Mr. Norman Hitcfaaan 



/s/ Edward M. Parker 

Edward M ■ Parker 
Chairman, Project BALANCE 



SECURI 








DEPARTMENT OF THE ARMY 

OFFICE, ASSISTANT CHIEF OF STAFF, G-3, OPERATIONS 

REGRADE D . BY AUTHOI^™™ 25 » D * °* 

O F CrU#* 5Z-1 AtjL 

3 Y Z O N ^/30/^ 2_ 

G-3 040 ORO (16 Dec 52) 8 January 1953 



SUBJECT: Technical Memorandum 0R0-T-160, "Operational Requirements for 

An Infantry Hand Weapon" 



70: Commandant 

The Army War College 
Carlisle "arracks, Pennsylvania 
ATTN: Librarian 



1. Transmitted herewith for your advance information is one copy 
of Technical Manor andum 0R0-T-160, "Operational Requirements for an 
Infantry Hand Weapon." 

2. This publication is a working paper of the Operations Research 
Office (Project BALANCE), in which consideration is given to the desired 
capabilities of a modern rifle. The Operations Research Office makes 
one particular recommendation already approved by the Chief of Staff, 
i.e., "that a m a.U (but adequate) number of experimental weapons, in- 
corporating the desirable characteristics enumerated, be manufactured 
anfl tested by the Ordnance Corps, in order more conclusively to determine 
the military value of the suggested features." 

3. Request that appropriate comments on this Memorandum be sub- 
mitted to ACofS, G-3 (RRScSW) for consideration by the Director of the 
Operations Research Office in the preparation of the final report. 

FOR THE ASSISTANT CHIEF OF STAFF, G-3: 



1 Incl 
ORO-T-160 






Brigadier General, GS 
Deputy ACofS, G-3 for 
Research, Requirements & Special Wpns. 




UNCLASSIFIED 



si